I've personally turned to Discord from Skype as much as I could regarding Disco because I've found I can pretty much do almost everything in Discord what I could on Skype, better. Faction-related e-chat, indy chat, official chat, HC chat all in a single faction server instead of cluttered randomly in a single list of conference calls, in short, better organisation.
Plus a functional browser interface. Plus TeamSpeak-like dynamic voice chat instead of conference calls. Minus russian spambots. Minus quoting in vanilla Discord. Quoting is the only feature I miss. Maybe one day I'll start using BetterDiscord for that.
I've never got lost among the Discord servers I'm on any more than among the Skype conference chats I'm in, and I've no clue how some people manage that. With Discord's overall better organisation such does seem to be counter-intuitive for me.
Even then I still use Skype because of a dev chat I'm in, even though a while ago I've been told the Dev Discord chat is already being set up. I do wonder what's the progress on it.
EDIT/PS: Posted this from an old craptop which can run Firefox well enough to allow using Discord properly, while the Skype client crashes upon startup.