They’re all fun in their own way - if you’ve never even tried another character, I would highly recommend taking one at least far enough into the game to get a few skill points and see what you like about their action skill. There may be one that you just don’t care for, but at least you’ll be able to say exactly what you don’t like about it. Highlights for me with non-Axton characters:
Maya tossing mobs around: Thoughtlocking the first enemy triggers Converge, which pulls all the other enemies onto him. Helios procs, which roasts them, and Ruin procs, which shocks, corrodes, and slags everyone in this mob. They are not focused on you, so they start laying into each other. Fire a couple of rounds into the mob, which most of them share due to Chain Reaction, and which triggers Cloud Kill, which starts roasting the slowly dispersing mob. The original target dies, the orb immediately re-acquires another target via Sub Sequence (since the enemies are still close together), and Converge re-groups them, Helios re-roasts them, Ruin re-electrocutes, corrodes, and slags them. However, before the mob dies, and because Blight Phoenix is up, you go strolling into this seething mass of softened enemies who aren’t really focusing on you, and you add to the roasting and corrosion. Because Sirens.
Gaige and shock kills - Grab the Storm and headshot an enemy. The enemy takes shock damage, enhanced by Wires Don’t Talk. Interspersed Outburst fires for bonus damage and the target is now slagged. The shock orbs surrounding the target apply electrocute damage, which is enhanced by both slag and Wires Don’t Talk. This electrocute damage procs Electrical Burn, which causes the target to catch on fire, which is also enhanced by the slag.
Zer0 stacking all his damage buffs into a single shot. Slag your target, swap to a Landscaper, and fire it at the ground (with Tw0 Fang helping unload the magazine quickly). Keep yourself near the target within melee range and let them hit you to proc Counter Strike. Immediately fire Decepti0n such that the hologram is between the target and the nest of Landscaper shot, but close enough to the target that it’s within melee range (so the target doesn’t back away), toss Kunai while maneuvering behind the enemy, and Execute. If you time it right, the following go into this hit (here’s a blow-by-blow play):
Slag increases the melee damage.
The Decepti0n timer increases the melee damage.
The Counter Strike timer should still be up from when you got hit for more melee damage.
The Be Like water timer should still be up from the time you shot him with the slag weapon for more melee damage.
Backstab gives you a melee damage bonus because you hit him in the back.
Ambush gives you a melee damage bonus because he’s paying attention to your hologram, not you.
Like the Wind gives you a melee damage bonus because you’re moving (via Execute).
Headshot gives you a damage bonus because you hit the enemy in the critical spot.
Iron Hand gives you a passive melee damage bonus.
Death Mark increases the damage from this hit because you hit the target with Kunai earlier.
This melee strike starts your first stack of Rising Sh0t
This takes a pretty good chunk out of the enemy’s health, knocking the enemy back. Because you’re an ace, you’ve lined the enemy up with your hologram and the pile of Landscaper shot. Because Decepti0n ended, Unf0rseen triggers, applying shock damage to the target in mid-knockback. Unf0rseen damage is enhanced by Death Mark and Slag. The enemy now flies into range of the Landscaper shot, which explodes one at a time, each explosion adding another stack to Rising Sh0t, further increasing their damage (in addition to being enhanced by Slag and Death Mark).
These are just examples of the many things you can do with some other characters during combat… give 'em a spin yourself.
edit - here’s a video of this shot with Zer0 (minus a couple of these mechanics: I don’t have Be Like Water nor Like the Wind, and I miss the Counter Strike timer and don’t get a critical hit, but you get the gist):

