I play Hunter but only Survival, so this is written exclusively through a Survival player's perspective.
I have fun with it because of the sheer versatility allowed by its kit; you can, amongst other things, basically fight at any range you want and also completely dictate the flow of a fight through choosing when to engage or disengage and well placed traps. You can pretend to be a Warrior and fight full-on melee without any fears or feel like you're still using a bow and only fight from distance with dots and kill command. Heck, you can even dual wield two Elemental Force 1 handers and do nothing but cast dots. This however comes at the cost of someone else's fun because what I just described is a spec that belongs to an overtuned class whose kit is miles ahead of anything else in the bracket. For this reason, as much I have fun playing my bouncy Survival that can keep moving around indefinitely while never losing damage uptime whatsoever, I decided to move on and play mainly Fury Warrior instead.
And oh boy, what a great choice it was.
Fury is often seen as an underdog spec that can't compare to Arms, so it is never expected to perform well. This leads to some pretty fun situations where people get suddenly 100-0'd by a double crusade Rampage with no chance to react. Needless to say, it is amazing when this happens. Aside from that, however, Fury has some resource generation problems that make it clunkier and harder to play than Arms (mainly the lack of a second Raging Strike charge) and pretty much most specs, as this is rarely an issue. Due to this, managing your damage can be tricky because it is negative while stalling for crusader procs, but at the same time you need to spend your resource pool on Ignore Pain casts to be able to survive while farming the procs, which leads to a sort of risk x reward gameplay that is the complete opposite of the steamroll playing Survival is.
So to sum it up, Fury feels rewarding to play because of its chaotic resource management. It is also very fucking easy to kite (MM Hunter and Arcane Mage are impossible MU's, you just quite literally get kited to death), so trying to maintain the Rage bar filled up is a challenge in and out of itself. But when the spec works, it usually results in some very compelling wins. In other words, a win on a Fury Warrior gives you a feeling that you worked for and earned it, while a win on Survival feels like the spec piloted the game for you.
tl;dr - While Survival is fun its sheer overpowerness removes any sense of reward and skilfull play that can be found in other specs.