Their ground games both have the same premise (let your projectiles control places you can't be), even if they are implemented differently. So in that respect, they're really close in terms of stage control and approach (or not) options. Snake kills early and dies late, but he has relatively poor mobility and no air game to speak of. Diddy dies at the average percent and kills late, but he has ridiculous mobility on the ground and in the air, and he has a very strong air game. Not to mention a command grab gives him an excellent option against shields when he's in the air. This is something Snake lacks.
So basically, while Diddy has all of these strengths, Snake's only real plus other than stage control is survivability. Of course, when you consider that his recovery is mediocre at best, even this isn't all that much of a plus. In most match-ups, Snake is doomed to be responsible for a large portion of the damage he takes if he finds himself off stage, which kind of defeats the whole purpose of dying late.