I read the Appendix to Jacob Neusner's Comparative Midrash: The Plan and Program of Genesis Rabbah and Leviticus Rabbah. The Appendix is entitled "The Two Principal Theories of Comparative Midrash." Actually, however, Neusner discusses three scholars: Rene Bloch, Geza Vermes, and Steven Fraade.
Comparative midrash is "comparing what diverse groups say about, among other things, the meaning of biblical verses" (page 187).
One reason that Rene Bloch thinks that comparative midrash is important is that it can help one to provide a terminus ad quem for undated Palestinian rabbinic traditions. Suppose that there is an undated Palestinian rabbinic tradition, and the same tradition is in "texts external to Palestinian rabbinic Judaism which have at least an approximate date" (page 188). What we learn is that "the undated document contains materials that circulated prior to a certain date" (page 188). Neusner doesn't "see much in that discovery worthy of celebration" (page 188). Bloch also advocates comparing rabbinic traditions with those in Philo, Pseudo-Philo, Josephus, the Septuagint, the Peshitta, the Qumran documents, the New Testament, ancient Christian writings, and liturgical sources. But Neusner questions whether this is truly comparative "midrash"---comparing different exegetical approaches to a text---or if it is instead a comparison of different legends and stories.
Neusner's problem with Geza Vermes' approach is that he ignores "the documentary setting in which an exegesis occurs" (page 195), as he focuses instead on "the exegesis and the date of the document in which it occurs, without further attention to what the compilers or authorship of the document wished to accomplish by making use of the saying or exegesis" (page 196). I do think, however, that Geza Vermes says something important, in the quote that Neusner provides: "The differences in its application at various periods may result from changes in aims, needs, or even doctrines; but such changes cannot be detected without knowing what exactly has been altered" (page 194). My impression is that Neusner and Vermes overlap in their insistence that comparative midrash should look at how each document interprets a biblical text, and determine why it interprets it the way that it does.
Steven Fraade wrote about the history of interpretation of Genesis 4:26, which says that people began to call upon the name of the LORD in the time of Enosh. According to Fraade, Christians tended to interpret the text positively, in accordance with their view that there existed in human prehistory a church that was not specifically Jewish (since Abraham and his seed were not yet called). But Jewish interpreters, including the rabbis, viewed the text negatively---as if it was suggesting that people in the time of Enoch began to mistreat the name of the LORD. That accorded with their narrative---that humanity was on a downward slope, until God selected Abraham and the Jewish people to play a redemptive role.
Neusner's problem here is that Fraade generalizes about the rabbis, and fails to consider the role of specific rabbinic interpretations within their historical contexts, such as the dominance of Christianity over fourth century Palestine.
Fraade does, however, say that we should consider how redactors make use of the material in their own way, with which Neusner heartily agrees. But Neusner faults Fraade for not following through on this.