I played both on Normal and only the stealth parts were that really got me occasionally. And I'm far from the best guy at twitchy shit.
Ah, you gotta play on Hard, man. I was joking about Easy because, really, the Normal is the new Easy in these games.
In Hard in Asylum, you don't get counter alerts. You do in Arkham City unfortunately, but it's somewhat balanced by those special enemies you mentioned... I have a feeling Hard is Harder because they add more special enemies per encounter as well as more gunners.
On hard, you need to really use gadgets... Grapple pull + punch is staple. Grapple pull + batarang is hilarious. There might be more gun enemies in Hard so you'd have to be thinking about how to disable them, whether grappling, disarm + break, throwing smoke at the enemies before you run in, or just targeting and attacking them up first - And they will pick up those guns as well as running to the gun cache (though that probably happens in Normal). One time there were two gunners standing right in front of a door you need to enter, and there's absolutely no way to stealth to them... I don't remember what I did, but throwing smoke at them might be the best option.
And then build up good combos for takedowns or even the stun one (I ended up using combo stun attack + beatdown attack to beat Axe-Man). Also, you
need to constantly "swoop over the fucking room to hit that one guy" because that is one of the main ways to position yourself away from the horde. And then I like to hit enemies about to attack me rather than counter sometimes, because that does more damage, which means I have less enemies to chip away at me when I miss a counter, and it especially means I have less distractions from getting at a Titan or heavy armored guys that you need to spend time doing a beatdown (well, I tend to just special takedown the armored guys), or Axe guy.
I'm not saying it's a super hard game, but it's sufficient enough that a gamepad will help. Maybe not a lot more than KB + M, but I believe it is more helpful to some degree.
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Side note: You seriously gotta just pick Hard mode for any game that comes out these days, especially console games. Unless it's Devil May Cry 3 or something. Avoid Normal like a plague.