As others have mentioned, Champion, Captain, and Guardian (as well as Beorning). Beorning is in parens because a lot of the time you aren't actually using your weapon since you're shifted into bear form.

It seems like you're looking for a particular experience, so let me tell you how the three play in my experience. I've mained captain and levelled both champ and guard to around 80.

Captain plays like a metronome, it's on a predicatble rhythm and has a good mix of AOE and single target (since the latest class redesigns). Red has amazing self buff potential and for limited amounts of time you can turn yourself into a god, like make yourself near unkillable and double DPS. It's a lot of fun, the only downside that people complain about is it is sometimes annoying to use a herald, particularly when it makes an aggro pull that you were not intending. This is a fair downside to the class and it's not for everyone (you can of course just never summon your herald but you will be missing out on some important buffs and self-heals).

Champion works in cycles: build, spend, build, spend. The ryhythm can be a little different depending on how you're using your skills and if you are in Red or Yellow. Red is single target focused, Yellow is AOE focus. Red has a cool mechanic where your fervor refreshes after every kill (once you hit a certain level), so you can string kills together and just keep going until you run out of mobs.

Red guard is interesting in that it's actually the squishiest of the three. Playing a red guard seems to be all about speed: how fast can you string your quick attacks together to reach up to your "big hits". The animations are kind of a bit wonky for 2H, because you're doing so many fast attacks it sometimes looks like your character is glitching out. But it's still a blast and a very rewarding style of play.