It depends.
I personally dislike scouring up the crust-infested walls of XBLA to find a suitable game to play all night with my friends. I would definitely enjoy it better if there were more games with co-op campaign possibilities.
But on the other hand, Online Multiplayer means you never have to settle for the quality of the AI. It's almost a must in any games of the "Competition" assortment, like racing or first-person shooters. But the significance of this quality is reduced when you realize those kinds of games are pretty cookie-cutter in the first place.
Overall, if you want an emphasis on profitable, replayable, or just individual fun, Online is the way to go. If there's an emphasis on "fun for the whole family", socializing, or simply more lasting fun, go Local.
To bring up examples, games like Warcraft III beg for Online. It's easily moddable, and that naturally means a lot of mods to be shared and partaken.
A game like Castle Crashers is funny and clever. It has some obvious flaws, but it's definitely the kind of game you want to play with your friends.
I'm personally skewed towards local multiplayer, because I have a brother with whom I enjoy gaming.