Differences in Approach or Implementation Status
Some of the libraries have seen more extensive development than the Omega Library in the early 2000s, and in many places has much more sophisticated algorithms. In particular, users have reported good results with the Cloog code generator (both in terms of the code generated, and in terms of ability to control trade-offs when generating code), and with the algorithms for counting integer solutions (Alexander Barvinok's work requires a vertex description of the polytope, which is not supported in the Omega Library).
There are several other points on which the frameworks differ, specifically:
Read more about this topic: Frameworks Supporting The Polyhedral Model
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