Just to confuse you, I'll start off with what I like: they're buttons to press that don't interfere with the GCD and normal rotation.
Okay problem time:
I like to press buttons and have something happen. Maybe someone gets a buff or something mean gets hurt. Whatever it is, the button press does something. At worst I get a one minute timer and wait for a big burst of damage (curse of doom can be fun, and had some big uses for soloing things that are not meant to be soloed back in the day).
On next swing is more like Press button, nothing happens, something happens. Huh? I didn't do anything, why did I suddenly get a yellow attack? Oh... a second ago I did something. That's like having a cast time without a cast bar or mobility restrictions or... well now it sounds pretty good. But that cast bar means I'm doing something. On next swing means I'm trying to do something but only waiting will make it happen.
This is one of the things that didn't appeal to me when I tried CoH on my friend's computer. As far as I could tell, things queue and cast as they come up. This makes it less button-mashy and less timing-dependent, which seems nice, but it also feels less interactive. I felt like I didn't make anything happen; I wasn't a superhero, I was watching someone else be a superhero as I tweeted suggestions and he'd respond as he got them.
Ah, there's the big one, on next swing feels exactly like horrible lag. I'm sure you've seen the condition when you cast, nothing happens except you see the GCD spin around, and then you go and press another spell and again nothing happens but the GCD spins and then the spell button lights up as if to say "I'll cast this and that once I can do something."
On next swing attacks are blatant pandering to the Lag lobby.
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