Ok, im just going to play devil's advocate here and say Peter could grab the win.
Aside from Peter having the LS stat (being roughly 45 times stronger) as mentioned earlier, Peter has a few things going for him that could nab him the win. For starters, his standard arsenal (equipment) is more dangerous than Homer's own, having access to weapons such as sniper rifles and shotguns while homer for the most part just has pistols. Homer COULD get access to such weapons with his optional arsenal, alongside stuff such as tasers and his radiation (abilities? Item? Doesnt say), but that would mean allowing Peter to be granted his OWN optional equipment such as the powers he got from Death, which would still allow Peter to come out on top.
Speaking of powers, Peter has many abilities that could nab him the win.
- For starters, his duplication allows him to clone himself up to at least 24 times, meaning that even with homers better martial arts skills the latter is just simply overwhelmed, even more so once you factor in Peter's greater LS.
- He can also BFR Homer thanks to his "Shadowy Friends".
- Peter can teleport, offering him a layer of mobility Homer can't match even with the latter's acrobatics.
- Peter also has better body control than Homer due to his variety of feats such as being able to turn into a ball.
- IF death's powers are allowed as part of the optional factor I mentioned, Peter could just insta-kill homer. Granted, Homer can ressurect, but with Peter being given enchanced stamina and his death touch, it would be hard for Homer to even attack him, given that he can't attack Peter in melee due to the death touch and the fact that Peter has taken gunshots without much issue, so Homer's gun's would just be dead weight here. So it would just end up in a stalemate for the most part until peter finds a way to knockout peter.
As for Homer's abilties, he's definetely better in martial arts in most regards, given his training plus his pressure point skills, but said fighting skill is often inconcistent as quite frankly, he's a moron. Granted Peter is also as well, but in the latter's case it often plays up to his abilities, such as teleporting to another car just because he wanted to watch the film playing inside it. Homer being able to use his MA skills and pressure points seems unlikely when he's also as likely to just straight up forget it. Meanwhile Peter, while not as skilled as homer, is still a capable fighter, as well as a somewhat more concistent one given his running feud with Ernie the Giant Chicken, so he likely has overall more combat experience. Additionally, most of Homer's combat abilities such has his elec manipulation and radiation are optional equipment, so he's unlikely to have it unless Optional Equipment is allowed, which in that case Homer would still be outclassed given Peter's own optional powers.