I've been through the previous Ace Attorney games (even played the Harvey Birdman: Attorney at Law game), and this one is my favorite so far. For the uninitiated, this series is basically an extremely streamlined version of those old mouse click-based adventure games, focused on legal cases of the protagonist attorney character.
While the previous entries in the series had Phoenix Wright as the title character, this fourth release has a new lawyer, Apollo Justice. Of course we'll see plenty of Phoenix is this episode, although in a very different role!
Maybe I'm just getting used to the crazy universe of the game, but the stories in this game started to make sense in their own idiosyncratic way. I only had to look up one thing on Gamefaqs - I did not manage to catch a tic of a character during the cross examination process. I swear, the last case even felt like a fantastic page-turner thriller.
Of course you still have the colorful, crazy characters, bad jokes, and funny references throughout the game.
For newcomers to the series, probably I'd recommend this entry as a starting point, just because the cases make more sense this time.