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.
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.