Due to circumstances involving needing to contact someone and them only leaving a Discord invite link, I ended up trying it. It wasn't fun, or pretty.
Now, of course, I'm not about to put nonfree software like Discord on my main machine, so I got out one of my spare laptops - an IdeaPad S10e running Windows 8.1 Embedded. It is by no means powerful, but it's fine for daily use - I can quite happily use ssh/vim/latex/LibreOffice on it, watch native resolution video, etc. on it. As far as specs go, it has an Atom N270, 2GB of RAM, Intel GMA graphics and a 160GB 5400RPM hard drive.
So, I opened up Firefox (57, even!) and copied the link from IRC into the address bar. The indicator spun, and then stopped. Not as in it finished loading. It froze before it finished loading.
For kicks, I opened up the task manager and watched in horror as both threads were maxed, the memory usage climbed from 500MBish to 2GB and beyond. The disk thrashed quietly as Discord finished loading its UI, and I looked in horror to see that it didn't fit properly on the screen. I zoomed out - slowly, as it took no less than 5 seconds for it to re-render each time.
So, I put in the first username that came to mind and joined. It took a good 30 seconds for everything to show up, and then I set to the task of navigating the obnoxiously wasteful interface on a 10" 1024x576 screen. After a bit I found the button to join the main text channel and started typing. Then I stopped, as nothing had showed up. I waited another few seconds, and then slowly, the text box filled. Within 15 seconds it'd caught up with all 30 characters I'd put in. So, I finished writing and sent my message, and went back to my desktop while I waited for a response.
I heard a strange, stunted noise, like music from a CD player in a car skipping. It couldn't even manage to properly play the notification sound due to how resource-starved the laptop was. Incredible. I finished up my conversation and closed the tab, and the fan went quiet.
I'd say this is a pretty good explanation of at least part of why I don't like Discord. The user experience is terrible:
I wasn't even using the proper Discord client, which uses even more memory thanks to just being Discord running inside Chrome.
Oh, and I didn't even mention the possible privacy issues