The difference is in the overall approach to hermeneutics. Basically, Keener follows evangelical approach to hermeneutics while Archer is heavily influenced by contemporary literary theory. I'll try to explain the difference in these 9 brief points.

1. Both Keener and Archer are continualists, to be sure. They both believe in Spirit baptism for today. Archer comes from holiness Pentecostal tradition, Keener defines himself as “Bapticostal” (by which he means “Baptist who acknowledges and practices spiritual gifts”). They both speak in tongues, have (more or less) high view of Scripture and affirm the importance of the Spirit's leading in interpretation. In order to understand the difference, you must understand development in Pentecostal theology in the last 40 years and how it was influenced by developments in biblical studies and in philosophical hermeneutics. I will summarize this in the following basic points.
2. Quick timeline.
   • [1910's] At the beginning, Pentecostals were neither liberals nor fundamentalists. They just wanted to read their Bibles faithfully (unlike liberals) and experience in in their lives (unlike fundamentalists, who were mostly cessationists).
   • [1940's] As the Pentecostal movement grew, it realized that it has a lot in common with evangelicals. This sentiment has prevailed within the movement and is probably dominant up till today. Pentecostals just mostly understand themselves as “evangelicals with tongues”.
   • [1970's] Some evangelicals (e.g. James D. G. Dunn) began to critique Pentecostal understanding of the doctrine of Spirit baptism and the initial evidence. It may sound funny, but Dunn never was anti-charismatic and his initial arguments against Pentecostal understanding of their doctrine were meant rather as academic exercise rather than a devastating criticism. Reaction to this critique, however, gave birth to the first generation of rigorously trained Pentecostal scholars and educators. At the same time, the evangelical mindset that was behind Dunn's arguments was transposed onto some vocal figures within the movement, namely Gordon D. Fee. Fee is vigorously Pentecostal in his practice and much of his teaching, but he has questioned Pentecostal views on subsequence and initial evidence. His bestseller How to Read the Bible for All Its Worth is a magnificent demonstration of evangelical biblical scholarship, not of Pentecostal scholarship.
3. How so? And why does Gordon Fee matter? Well firstly, Keener is Fee's “spiritual heir”. He basically replaced Fee on his position of a strong “evangelical Pentecostal” voice. They are both Pentecostal in their spirituality and ethos but evangelical in their doctrine and scholarship. The hallmark of evangelical scholarship is the combination of (A) the high emphasis on objective historical research as the first step in exegesis and (B) high view on the Bible. A typical conservative evangelical scholar is nothing more than an (imaginary) German liberal higher critic with high view of Scripture.
4. Archer, on the other hand, follows a different strand of biblical scholarship that has been developing in literary studies over the last 100 years and has slipped into biblical studies within the last 40–50 years. Archer builds heavily on hermeneutical principles that were designed by Hans-Georg Gadamer and Paul Ricoeur. To be extremely simplistic but essentially correct, this school of thought basically says three things:
   1. Texts have their own lives after they are written. By looking on a (biblical) text, you're not looking at Paul's or Isaiah's writing. You are looking at the Epistle to the Romans or Book of Isaiah that comes to you translated, endowed with rich tradition, relevant to your time in some manner, functioning somehow within your understanding of redemption, etc.
      
   2. There are three layers of the (biblical) text. (A) Behind the text lies the history, archeology, the real Isaiah and Paul with their respective ancient circumstances and mindsets. (B) Within the text are intertextal links, text's inner structure, narrative patterns, allusions to other texts, etc. (­C) In front of the text is your 21th century world, your challenges, wishes, your mental setting.
   3. Every interpretation must start at the interpreter's “horizon”, i.e. in his/her specific situatedness, because everyone approaches the text as a person of race, gender, culture, social status, personal preferences and problems, etc. And although one may partially discern his/her situatedness, it is never possible to wipe it completely. But is it to the detriment of my interpretation? Perhaps not! Perhaps it is me, after all, who determines the meaning of the text through the text itself. Am I not in need of relevant meaning here and now? And is it not me who determines that need? Now if the text is so burdened with interpretive tradition anyway and if the original meaning isn't within my reach (and when it is, it's irrelevant to my need), why should I bother with the classical approach “see what it meant and then determine what it means”? Indeed I should not! Because it is my need for relevance that determines the whole interpretive process and the text's role in this process is only to serve as a field on which that relevant meaning will be found.
5. Now please notice that Fee or Keener are not philosophers, they're bible scholars. Keener's Spirit Hermeneutics is a one-shot attempt to cover it all and although I do see a good merit in that book, I think that it leaves a lot of questions unanswered. Nonetheless, Keener basically says exactly the opposite of what was explained above in points 5.1–3. He does affirm situatedness of our present reading and in fact, he encourages interpretive diversity, because some cultures may be more natural readers of some parts of the Bible than others. (E.g. bedouins could understand Abraham, colonial victims understand oppression, etc.) He also affirms role of the Spirit in interpretation. But he is implicitly but consistently adamant throughout his work that there is the original inspired meaning in the Bible that can be unearthed by exegetical methods old and new that the Spirit will never contradict. This places him safely within the ranks of evangelical interpreters.
6. Moreover, Keener openly advocates E. D. Hirsch, who is the major opponent of Gadamer and his legacy. Hirsch's philo­sophical approach is much simpler and more transparent. He openly and completely refuses to talk about “horizons” in gadamerian terms or about lives and layers of texts. He simply says that the text has its original meaning and contemporary significance, nothing above or between that. If you secure the former, you can contemplate the latter, not vice versa! This is what most evangelicals affirm and exactly what Gordon Fee taught in his How to Read the Bible for All Its Worth. Fee would probably add this: If the Bible in its original meaning doesn't speak about your contemporary problem, then it is simply your problem. You could obviously find an answer to your problem by studying biblical principles and theology, but you should not read the Bible through your problem/experi­ence/situation.
7. To be sure, one should not equate evangelicals with Hirsch and Pentecostals with Gadamer / Ricoeur. There is a variety within both movements. Many classical Pentecostals follow evangelical interpretive principles (e.g. Robert P. Menzies) even without buying into Fee's dismissal of the doctrine of initial evidence. As far as evangelicals are concerned, a strong evangelical school of thought has been formed around Anthony Thiselton whose life legacy is paving a wide and easy way towards Gadamer / Ricoeur in evangelical biblical scholarship.
   When it comes to Pentecostals, there seems to be a factor enfant terrible - naughty child factor. A good deal of deep and careful historical research has been done in the last 40 years in the origins of Pentecostalism that seems to indicate that Pentecostals are not and have never meant to be “evangelicals with tongues”. This means that they should stop adopting all the conservative evangelical textbooks, make their own way out of evangelicalism and establish their own firm theological tradition, such as Catholics did after the councils, Orthodox did after the schism and Lutherans/Reformed did after the reformation. For some this is difficult to acknowledge because “evangelicalism” seems to be able to be pretty wide-tent. It is sometimes funny what a person may teach or do and still be regarded “evangelical”. But those Pentecostals that deem it necessary to leave evangelicalism and establish a Christian tradition of their own are often welcoming Gadamer / Ricoeur and the postmodern schools of literary criticism, because they see it as an opportunity to build Pentecostal hermeneutics upon new foundations. I would say that this idea is short sighted and that Pentecostals should base their doctrine of the Word of God on theological principles of their Pentecostal distinctives. That is, however, for another story.
8. So to summarize the difference: It is safe to say that Fee and Keener do use historical grammatical method and that Hirsch backs it up philosophically. This approach could also be named simply “historical approach” and sometimes mingled with “historical critical method” or “higher criticism”. The difference between grammatical historical and historical critical method is only in different appreciation of the doctrine of inspiration and inerrancy of the Bible. But philosophical starting points are the same. It is connected with modernism, which stems from what they call “the Enlightment project”. The central tenet of modernism is simply this: The truth of interpretation, revelation, science does exist and we can find it.
   On the other hand, people like Archer are backed up by Gadamer / Ricoeur and they do not encourage historical approach as the only way for attaining the truth. You'll find good deal of criticism aimed at historical grammatical method in Archer's book. Archer calls for his “Spirit, Scripture, Community” approach. It might be described as “reader response approach”, but in a very specific way. I'll get to it in the next article.
   Archer would say along with Gadamer that one should start by discerning both horizons: horizon of the text an horizon of the reader. Then these horizons must be be fused. Archer writes: “The hermeneut must be concerned with more than only the horizon of the text. This author [Archer] asserts that any hermeneutical strategy must negotiate the tension between the two horizons (the horizon of the text and the horizon of the reader in community).” (Archer 2009:209) This paradigm allows Archer to advance what he wants to advance. To do proper justice to Archer, I should add that he is synthesizing a significantly altered hermeneutical framework whose objective is not to apply Gadamer wholesale, but rather to devise a hermeneutical approach that would be as Pentecostal as possible.
9. You'll be able to understand much more about the difference between Keener and Archer after reading Archer's review of Keener's book. (See #1 in bibliography below.) Volume 39 of Pneuma journal is largely devoted to reactions to Keener's book. Articles by Waddel & Althouse, Oliverio, Spawn, Mather, Aker, Grey and Keener are quite valuable as they disclose who is triggered by what and why. Archer's book on Pentecostal hermeneutics is also very readable and very valuable. So this is a basic bibliography on the subject:
   1. Archer, Kenneth J. “Spirited Conversation about Hermeneutics: A Pentecostal Hermeneut’s Res­ponse to Craig Keener’s Spirit Hermeneutics.” Pneuma 39, no. 1–2 (January 1, 2017): 179–97. DOWNLOAD.
      
   2. Archer, Kenneth J. A Pentecostal Hermeneutic: Spirit, Scripture, and Community. Cleveland, TN.: CPT Press, 2009. DOWNLOAD.
      
   3. Keener, Craig S. Spirit Hermeneutics: Reading Scripture in Light of Pentecost. Grand Rapids, MI: Eerdmans, 2016. DOWNLOAD.