I have been a part of a Discord server for a (non-Keen) fangame for about a year (as well as a couple of other servers here and there) and a mod for a month or two, and I've got to say, it's pretty great. The only complaint I ever had was that it was missing a search function, but they implemented one a while back, so it's pretty much perfect. And yes, the whole chatlog stays there indefinitely.
In addition to the features Roobar listed, admins (or people granted this right) can add custom emoticons or emojis or whatever people are calling them. And yeah, granting privileges is very... modular, I guess? You can pick and choose things
for the target user and make your own roles. We have one person who only has the power to add new emotes because that's what they're good at (and it's entertaining when it happens).
You can make audio channels if you're into that but I've never messed with it because I can't stand the thought of people hearing my voice. But it's there!
I'm sure there are more benefits...
I say all this despite never having been to the Keen IRC (or any IRC on that site). I also think it's understandable if you don't want to move to a newer platform for reasons of nostalgia or the like. I just thought I'd put in my two cents as someone who has been communicating primarily via Discord for the last year.