Is there a good, coherent story here? It's hard to tell because this omnibus organization is such a wreck that I'm not convinced I want to keep it instead of the individual volumes. (I think my answer is that I won't.)
The problem is that the original AvX collection was already a mess because they separated out the main miniseries and the short fights AvX comic. For these omnibus they maintained that and they just stacked all of the crossovers on the back. They even choose to keep the crossovers in arcs rather than integrating them. It's a mess to read. You're constantly going back and forth over the story line, which is why this omnibus has no value as an omnibus. If they're not going to try and tell a story, then you might as well just have the individual collections.
Marvel is usually much better with their omnibus mapping. This is deeply, deeply disappointing.
As for the story: not one of the best X-crossovers, not one of the worst. The core storyline is overly decompressed, mainly to have lots of big fights. The fights miniseries, AvX, is almost total trash (especially when you don't really see where they occur in the larger story). But a lot of the crossovers are pretty good. UXM, Bendis' Avengers, even the weird cosmic storyline in Secret Avengers: it's all worth read and some of it's pretty good. Then it all ends with Consequences, which is terrific.
I'm not thrilled by the mass character assassination that happens in the story (with all of the Phoenix Five being treated like criminals despite the fact that probably every hero in the Marvel Universe has been mindcontrolled into doing terrible things at this point). But the setup for the rebel-Scott-Summers arc is nice, as is the use of the Phoenix to deal with the No-More-Mutants problem.