We actually use both. Discord is great for "pinging" fleets, i.e. sending out a bat-signal to all members that a fleet needs to form for whatever reason. It's also good for general text chat (talking about market/industry/memes). If the corporation you joined was small and not a member of a larger alliance, then they may not have needed Mumble.

However, if you join a large alliance/coalition, fleets can easily get to 100+ player counts, and a single discord voice chat room becomes unusable. It is extremely important that you follow the fleet commander's instructions during a fleet. That is where Mumble shines with the fleet commander residing in a top level voice channel, with other members in lower-level voice channels that he cannot hear. It also allows for lower-level members to join voice channels designated as "quiet", so you don't have to listen to the chatter of 100 drunk Eve players during a Friday night fleet.

Discord is generally used for day to day chat in corps, then you'll be told to get on Mumble for fleet ops. Some corps continue to use Discord for small fleet ops but as soon as you're doing ops with Alliances or blue corps you'll nearly always end up on Mumble.

Lots of corps use discord, but at an alliance level you'll often end up with mumble for comms. Another 'dead' open source software that's used is Jabber (XMPP) for 'pings' aka broadcasts to tell people there's a fleet up.