Ok, im going to be the Devil's Advocate here. I'm going to make a case for why Sonic wins this, because at this point why not?
Now, as some people already mentioned, Sonic takes the advantage in various Aspects. Aside from the AP difference, Sonic is faster thanks to various speed amps, is invulnerable, can resist Bug's plot manip and his time stop powers get past Bug's resist to time stop. However Bug's has a lot of advantages Sonic can't overcome. At least, that is, on a surface level. However I think's Bug's advantages are not as great as they seem, and I want to discuss why that is the case.
Bug's Immortality
So the big issue here is that Sonic (allegedy) can't really hurt bugs, as aside from Bug's insane regeneration, he can also resist the negation of said regeneration, both of which is at a higher scale than Sonic can't handle. So it sounds like an inevitable loss for Sonic right.
Almost, but the to understand why, we need to understand the logic on toons operate.
See, part of how toon force regen works in the world of Looney Toons is that aside from being able to regen, none of the toon character's actually feel any pain and are invulnerable to damage, with most showcases of them being pain being mainly done for comedic effect rather than actually being hurt. In short, Looney Tune characters are not only Immortal, but also Invulnerable (in a loose sort of way, in that they can be damaged but not actually be hurt).
This detail is ultimately the reason why Sonic edges out in this regard. See Sonic's Low Godly regen negation may not be able to overcome Bug's High-Godly regen (even disregarding Bug's resistance to High-Godly regen negation
say that five times fast) the Super Form is capable of Negating Invulnerability of Bug's Bunny, allowing the rabbit to experience something's he's never really felt before:
actual pain in an actual fight. With this and Sonic's obvious stats advantage, Sonic may not be able to kill Bugs, but he can sure as hell leave him in an actual world of pain long enough to be knocked out for the count, being both stronger and faster than the rabbit can handle.
Bug's Toon Force vs Sonic's Hax
Oh **** my fingers
Ok, im not going to go forever about this, its no suprise that the sheer power of Toon Force vastly exceed's anything Sonic has fought against and vastly exceed Sonic's own range of Hax
THAT BEING SAID, Sonic has a variety of resistance that just about make most, but not all, of Bug's Toon Force shenanigan's a moot point, while also providing some hax that Bug's himself can't resist.
Removing any hax that Sonic can resist as well as the ones that only apply to Bug's , the only Toon Force abilities that can affect Sonic reliably are:
- Adhesive Manipulation (With ACME glue)
- Perception Manipulation
- Broadway Force
- Supernatural Luck.
All these hax aren't bad per se, but they're unlikely to work on Sonic for various reasons. For the adhesive manipulation, it simply because it would require Sonic to get stuck to it, which isn't that likely considering Sonic can fly. For the other 3 however, while they all would definetely work on Sonic, they aren't like to take affect simply because Sonic is much faster thanks to his speed amps.
Bug's hax and toonforce generally work around character's in his universe because most of them are equal to him speedwise (or they are inferior, given that Bug's is one of the top tiers), so against a individual who is much faster than Bug's can act, its unlikely he would be able to have those advantages take effect before Sonic makes Bugs roadkill, and it would be unfair to suggest that these abilities can act faster than Bug's reaction since they require Bug's to do something most of the time first.
The Supernatural luck is also inconcistent, so its not a full guarantee it could activate in this fight even if it was faster than Super Sonic.
Sonic isn't entirely without his own hax though as he has a few hax that could give Bug's trouble, but the biggest aspect is likely the Cyber Corruption which he manages to control and wield by the end of Sonic Frontiers. For all of Bug's power and resistances, he lacks specific resistances to Info and Memory Manipulation, which could likely impact him in the long run as the Corruption would force Bug's to gradually forget himself, which would in turn cause him to be unable to use most of his toon force powers. It would also likely paralyse Bug's as well, but given that Toon's can paralyse others it would be possible that Bug's mastery over his toon powers would make him able to resist it.
Intelligence factor
Bugs is definetly smarter, but Sonic takes it in actual combat experience. Also as mentioned before, Sonic takes it in stats, so while Bug's may have more brain, he would be relatively too slow to use it. Also as mentioned previously, Cyber Corruption would also come into play here which would affects Bug;s intelligence via Memory Manipulation.
Power Nullification and Power Mimicry
Not gonna lie, the latter could probably be trouble for sonic, but not the former, as while Bug's can nullify powers with Toon-Force, the Super Form can do the same with its Aura, and since neither character has a specific resistance to power nullification, it for the most part cancels out.
On the topic of Power Mimicry, while Bug's could and would be able to copy Sonic's powers, as mentioned before, the Cyber Corruption Sonic wields would likely come into play before Bug's could do so, with its memory manipulating effects impairing Bug's knowledge and ability to do so.
So with all that being said....my votes going for
Daffy Duck
...Wait, he's not a vote? Alright then, im putting my vote for
Sonic then.