I started Jonathan Goldstein's Anchor Bible commentary on II Maccabees.
dates I Maccabees to 90 B.C.E., Jason of Cyrene's work to 86 B.C.E.,
and the abridgement of Jason's work that we recognize as II Maccabees to
78/7-63 B.C.E. Goldstein offers various reasons for his date for I
Maccabees, but he believes that II Maccabees came later because it
appears to respond to I Maccabees----to dispute some of I Maccabees'
details. At the same time, Goldstein maintains that I Maccabees and II
Maccabees drew from a common source, for they overlap on a variety of
details, such as Jason's construction of a gymnasium.
I go into the ideological differences between I Maccabees and II Maccabees in my post here.
In this write-up of Goldstein, I'll mention two details that stood
out to me. First, Goldstein argues that II Maccabees does not regard
the Jerusalem Temple as fully chosen by God and thus recognizes other
sanctuaries; I Maccabees, by contrast, appears to dislike sanctuaries
other than the one in Jerusalem. Second, Goldstein maintains that I Maccabees and II Maccabees had different
approaches to the Book of Daniel (which Goldstein may date to the second
century B.C.E.). I Maccabees does not shy away from mentioning the
events surrounding Antiochus that did not transpire as Daniel predicted;
II Maccabees, by contrast, ignores those details or tries to show that
many of Daniel's prophecies indeed were fulfilled.