Having just started AAI...
I have to say I'm really digging it so far. The music is awesome, the cases are fun to solve, Edgeworth as a playable character is handled really well, the changes to the formula from typical Ace Attorney are welcome, and, in my opinion, in some ways improve on your ability to reason out conclusions on your own over the main series...
But then again, I've only just finished the second case. Apparently things sorta go to hell in the last case if my understanding is correct. Still, I'm having a great time with it thus far. I'm already enjoying it a lot more than AA2 and 4, which are the games it normally seems to be ranked with.