Another thing AAI has going for it is Lang and his "NOT SO FAST!" voice clip, and he's only in 2 of the 5 cases (technically 3, but yeah, not counting E-4). I guess Kay was all right, too. I still prefer AJ though. At least in AJ you sort of retain that "role-playing" feel, even if you're constantly being overshadowed by Phoenix. In AAI I sort of just felt like I was watching Edgeworth solve everything - in that regard, I think the game was hurt by Edgeworth being too smart a protagonist. Some people really latch on to Edgey, but I've always preferred him as an antagonist or rival. I don't really enjoy playing as him (although it was pretty cool in 3-5).
Both AJ and AAI have bad pacing during investigations, so I guess another reason I prefer AJ is due in large part to music. The general "walking around" music in AAI was really quite bad at times. If I'm playing a boring game, hopefully it at least has some decent tunes.