Just started playing (got the game today) and feeling the same way about Axion. Mind you I seemed to enjoy sniping more in the first game. Probably try a brawler next.
I haven't played my Axton much--I think he is at level 7--but bear in mind that it takes at least 10 or more levels to get a feel for these classes. Of course, they are all the same until you hit level 5, then you need to get into the 2nd tier of a tree to start having fun with them.
Of course, depending on how you build them, just about any class can eventually feel stale, as you get into a routine of playing into your build over and over.
One of the ways the game varies itself through the mobs--their different behaviors and such.
I've really enjoyed one playthrough with Zer0 and nearly one with Gunzerker, but the Siren is still my favorite (max level and all DLC/UVHM now). Mainly because a tricked out phaselock against a big mob is incredibly fun, and the dialogue you hear from mobs, as a Siren, is absolutely hilarious. Also, you will play Nomads very differently with any character other than a Siren, which can quickly expose and dispatch them (I remain frustrated on any other character...but there is always that "G" button, which triggers some more hilarious dialogue from Nomads)
Once you start taking out Goliath heads and sit back and watch them level up on their own allies, start listening to emo Nomads complain about everything and the ramblings of psychos that don't know you are there, the game offers enough detail to keep you going. For me, anyway.
....plus, it's truly about the loot. You have to really be into the loot mechanic to get into Borderlands games.