Bowser vs Eggman is gonna be close, but I feel like Bowser takes it in the end.
Eggman’s made some powerful robots and his armada could probably nuke the entire Koopa Troop, but the reason I’m leaning Bowser is simple: Fury Bowser.
It’s been shown that for as tough as Robotnik’s inventions can get, he can’t handle gods (or beings with god-like powers). Perfect Chaos, Solaris, Dark Gaia, The End, he couldn’t beat any of them. Fury Bowser’s destructive capabilities are immense, he’s nigh-invulnerable, and he’s pretty much Godzilla. I bet he could tank a missile barrage like it was nothing.
If it weren’t for Fury Bowser, Eggman would probably win. But unless he can get his hands on a Giga Cat Bell, I think Bowser wins in the end.
Now Super Sonic could probably kick Fury Bowser’s ass, but he’s not who we’re talking about here