Against the MUs that Bowser just gets rekt on Kirby seems to do a lot better, but against characters that rely heavily on pressuring with fast close moves (spacies, Doc, Pikachu, etc) I'd say Bowser has the edge by a bit since he has a really amazing OoS Up-B and CC options into VERY HIGH percents. Even though he can't edgeuard as well he's better on the ledge against some characters. Kirby's screen door of pain and Dtilt are a serious threats to Marth, Falcon, Spacies, etc. His FF dair edgeguard is actually really scary as well since it can be very hard to not get dragged down with it.
People also giggle at swallow-cides, but it still happens on any level of competition. The aerial swallow hitbox is laughabale and recedes inside of him but the ground hitbox on the swallow grab is massive and can catch like 90% or approaches from the air or ground. And if you are recovering it can be easy to forget it's a tool Kirby has, then it's too late and your getting released into the abyss.
I think if you had to go all Kirby in a tourney you'd fair better overall against all the top and high tier characters, Bowser has some of what I consider unwinnables (Marth , Peach, and Sheik can be a nightmare) and the rest he gets comboed too easily by.