Sound, grunt, especially exiting bends, looks & panache. Only ridden a triple once (150 Speed Triple) so can't really comment but I'm sure the triple owners can tell you more.
I'm now on a BMW 1150GS so still a twin (flat rather than v), just doesn't have such a sweet tone, and the engine looks hideous rather than seductive!! Handles miles better than the looks suggest though so I am more than happy with it.

Ducatis are generally L twins BTW as the angle is 90 degrees whereas the Aprilias are 60 degrees so are proper V twins ;D ;D