I'm going to say Bulbasaur has the edge here. Pikachu has a pretty decent speed stat, but it doesn't have access to many worthwhile moves. Let's talk about the build you'd use to pretty decisively beat a Pikachu.

Pikachu's common passive ability 'Static' means that it can potentially inflict paralysis when hit with physical moves. On top of that, Bulbasaur has a fairly high Special Attack stat, so it'd be a good idea for it to use Special moves rather than Physical. On top of that Pokémon get a Same Type Attack Bonus (STAB) for using moves that match their type, so we want a non-physical Grass type move. 'Leaf Storm' is probably the best move we could use in this case. To get a Bulbasaur with that move, you have to do some breeding, but it's totally possible.

Now we'd also want to take advantage of Bulbasaur's own common ability, 'Overgrow', which boosts Grass type moves' effectiveness by 50% when it goes below 1/3 of its HP which, combined with our STAB means Grass type moves are now 200% as effective. Of course once we get our HP that low we're going to want to avoid taking much more damage. Using Bulbasaur's 'Sleep Powder' move at this point will cause Pikachu to fall asleep, preventing any further attacks.

So we've got our basic strategy, get down to 1/3 of our HP, put Pikachu to sleep and then wail on it with Leaf Storm. While we're letting our HP drop we could use something like 'Swords Dance' to boost our attack stat as well.