Okay, this is actually pretty close since they're both my favorite Pokémon in their own respective sagas. First, Bulbasaur is at a disadvantage since it was in the Kanto saga, the saga where the writers didn't know jackcrap about how to really SHOW that Ash's Pokémon were strong. They mainly implied that all of his Pokémon were very powerful by simply telling us, and Bulbasaur had a lot of plot-device losses just so Pikachu or Charmander could win. However, at the rare times when things weren't revolving around Pikachu or Charmander, it is always Bulbasaur who scoops up all of Ash's wins, and usually in large quantities.
Swellow, on the other hand, was in the balanced Advanced Generation saga. He was in many epic gym battles and almost always won. He didn't have that many losses.
Back to Bulbasaur, we see lots of illegal moves on him, lol. Unlike Swellow, Bulbasaur had to build his character on the sidelines, most notably during Master Quest. In the Johto League, both Pikachu and Cyndaquil were owned really easily by a shiny Magneton, but Bulbasaur owned that Magneton as easily as it owned the other two. Then, it tied with its nemesis, that one pesky Meganium. If Bulbasaur is as powerful as a fully evolved starter, then we can tell that it may be on par with Charizard and Sceptile. When Bulbasaur came back in Advanced Generation, it cleaned up after both Charizard and Squirtle, defeating Dusclops and having a draw with Solrock.
So in the end, my vote goes to Bulbasaur. A lot of this post contains my opinions, so if you don't agree with me, I understand, but that doesn't give you a right to start a fight or yell at me.
Everyone is entitled to their own opinion.