Ok so having finished the game, i too wanted to weigh in on it.
The first hour or so felt a little slow for me, maybe it's because I'm coming from the background of someone who's played every AA but only about an hour of Layton prior, the Layton segment at the beginning needlessly dragged on for me. The game really hit it's stride during the first Ace Attorney segment IMO.
The Middle of the game was great. It was truly one of the best AA games and the puzzles, hint coins and Layton style of investigation blended perfectly with the cases. Much better than the typical point and click style investigation of AA. The only real problem I had was that everything was too easy. There were some head scratchers during the trials, but easily overcome with a hint coin (Which btw, there were way too many given out during the game.) The Layton Puzzles were overall just really easy. I barely struggled, and this is as someone who's barely touched a Layton game.
Following the 3rd AA court case in the game, I feel the game took a sharp downturn. The "big reveal" and everything leading up to it was incredibly stupid IMO. I'd honestly rather they pull the "It was all a dream" thing than do what they did. The whole thing is full of plot holes and frankly I recommend not playing past the 3rd case. Speaking of the ending, it dragged on IMMENSELY. It should have been like an hour shorter at least, it felt like needless fluff. Like others, I also noticed slowdowns throughout the game, however in this kind of game it doesn't bother me at all.
Despite that, the middle of the game was really something special and as a result the ending doesn't completely dampen my passion for this game. The music was superb (though not as good as Dual Destinies) and I liked the art style and the animations. Voice acting was overall done well and presentation was generally top notch. If I were to give a score, it'd probably be an 8/10. If I was rating the game up to the end of the 3rd case, i could really see myself giving it a 10/10. Overall, definitely worth checking out if you like the AA series (and probably the PL series.)