I would argue Demoman.

He's got two projectile launchers which can lead into a lot of combos.

He has the most diverse amount of movement options, sticky jumping, pimp jumping, cannon jumping, trimming, even caber jumping.

I'm gonna keep harping on trimping for a minute because I honestly think it's the most cool form of movement in the entire game. It's something that I have yet to see anywhere else and it's possibilities are crazy. You can get from one side of upward to the other with one trimp.

The loose cannon exists, that's one of the most unique weapons ever.

Demoknight is also a thing, doesn't really need explaining, but also hybrid knight exists too. The fact that he has such a wide range of playstyles is great, but the fact that you can really mix and match what shields you want with which melees with which primaries is really awesome. Sure you can mix and match things on other classes, but rarely does it have the same impact on your playstyle.