Real answer: Toonforce vs. Toonforce fights are not based on raw power and ability, but they do sorta have rules. It's like wrestling: One of these characters will wind up being the heel, and one of them will be face. The heel may or may not start off winning but the face will almost always get the last laugh. From there the determinate factor becomes what is the funniest way this can go down? And that almost always ends with the good guy winning.
If we look at it this way instead of pointlessly measuring toon feats which are fluid and don't make sense and don't matter, then it becomes obvious given both of their records that Popeye would be the good guy in this scenario and Bugs would be the obnoxious troublemaker. Bugs will start the short by getting on Popeye's nerves, it'll progress with Bugs being more of an asshole, and it'll end with Popeye knocking the spinach out of bugs, eating it, and punching him so hard he flies off the page and into a completely different cartoon.