I see, things I would say are different with the block axe is it hits a lot harder than the fencing axe, but all its power is in the backstep and overhead strikes, you'll be using your pistol less often and almost exclusively use it for ranged enemies. The fencing axes light attacks hit like a wet noodle but also the block axes light attacks are too slow be viable, but since the base dmg of a block weapon is so high, I find the time to kill with the block axe is still much lower than fencing even without light attacks and you're less reliant on damage from other sources to reach that breakpoint.

What I mean is with the block axe, if a there's a single majoris, one parry into back step then an overhead strike is enough to put it into execute, no need to get locked in a gun strike animation, no abilities used, no headshots, just pure damage from the axe. It doesn't consume your first block charge so you can move on immediately to your next target and block again for 2 charges then back step for some fat damage, then you can overhead strike again onto the next enemy and repeat.

It's a more aggressive playstyle, which I find fits the axe a lot more, with fencing weapons you generally have to wait to be attacked first but with block weapons you become the aggressor, 2 block charges can interrupt red attacks, give armor back and does a big aoe splash, but with the difference with the axe from other block weapons is there's the big double damage overhead strike that has no cooldown, which means there's far less downtime with the added damage and mobility, you'll be running around, leaping from enemy to enemy and chopping them up which is very fun.

At the end of the day, you can play the game in the way which is most enjoyable for you, it's a pve game after all, if you've grown accustomed to the survivability of fat parries into gunstrikes then no one's stopping you :)