Almost every single last case in any Phoenix Wright game is pretty sad. You don't get a truly happy ending, but instead, you end up re-opening past wounds and learning the bitter background of everyone involved. The "special case" of the first Phoenix Wright (The one where you're with Emma, not Maya) had Edgeworth resigning at the very end, while a bunch of characters such as the cowboy and Emma's sister are jailed. Even though everyone cheers in the end, well, it's not that happy.
Oh, there's plenty of sad moments in the games. Sadness is all over the place. But I still wouldn't call it emotional. I mean, as you mentioned, everybody cheers in the end. That's the thng. Ace Attorney consistently has this forward-looking attitude. You constantly have to set aside the emotion and carry on. I mean, really early in the first game, you're given a pretty nasty shock, but you're not allowed to feel bad about it. You have to go through the case and get the bad guy, forgetting about how bad what happened might make you feel. In a way, that's one of my favorite things about AA.
In that T&T case you mentioned, although finding out who the actual culprit is rather emotional, the thrill seems to wash over it completely. I remember, at the end of that case, I was just desperately caught up in the action and didn't have time to feel sad about the culprit. In fact, that very last piece of evdence you submit is just so thrilling, so "in your face" (is that a spoiler?), that I'm too excited to feel bad about it.
Most other stories, in their emotional moments, let you soak in the sorrow completely. They dwell on the sadness for a while and emphasize how bad the characters are feeling. Ace Attorney isn't like that. You're either too busy getting the bad guy or trying to ignore the sadness and be cheery anyway to actually feel emotional.
“These are my principles; if you don’t like them, I have others.” – Groucho Marx