When I focus my thoughts on the strengths, I would say Compilation of VII is better.
When I focus my thoughts on the weaknesses, I would say Ivalice Alliance is better.

Essentially, VII & Crisis Core were enjoyable games and VII is my favourite game of all time. On the flipside, Advent Children was (excluding the graphics) kind of rubbish and ruined some of my favourite characters. Before Crisis is something I'm unable to play and Dirge of Cerberus is something I've yet to play and have heard very mixed messages about from my friends, more negative than positive.

I've yet to play FFT (just bought it this weekend) or FFTA2. I've played FFTA and FFXII. I really liked both games but wouldn't put them on the same level as VII, although they do match Crisis Core.

If the games were comic book characters, Ivalice Alliance would be the original Uncanny X-Men (ie Cyclops, Angel, Beast, Iceman and Marvel Girl, all in their teens) and Compilation of VII would be Batman (VII), Alfred (Crisis Core), Robin (Advent Children), Batgirl (Dirge of Cerberus) and some other character who is in the wrong country and therefore can't get involved. Batman is incredible, Alfred is cool, Robin and Batgirl are meh and the other one is irrelevant. Meanwhile, the X-Men are pretty much always great. I'd back Batman to take on an individual X-Man, but even with Alfred's guidance, Robin and Batgirl just don't cut the mustard and as a group they'd probably lose to the fantastic teamwork of the X-Men.