That's gonna be a hard one, because they are both great games, but they have their own playing style( depends what you are in the mood for). You can also pick up Zelda majoras mask, and a cheap copy of phoenix wright for the nds
I definately would NOT recommend jumping into Dual Destinies as your first Phoenix Wright game. The game is much more enjoyable when you know the backstory to some of the characters. Like NicEXE says, definately pick up the Ace Attorney Trilogy first.
If you haven't played the old PW games, then definitely get the Trilogy, yeah. It's three games in one and it's awesome. If you played and liked the first PW games, then maybe get DD? I tried playing Majora's Mask, but couldn't be arsed to keep playing after I beat the first dungeon for some reason.