While I think they're both great, neither of them are an alternative to Discord.
Getting in? One click on email/URL and then sign up. Join a channel? One click. Voice chat? One click. Stream your game? One click. Seamlessly switch to mobile app? Done. I have yet to meet a user that can't get into it with just an invite link. It's amazingly user friendly. And if I want to, I can granularly create roles for users and administrators of arbitrary levels and access rights.
I share the privacy concerns, and that I can't grep any logs easily (though with voice chat that's harder regardless), but simply from a user perspective if it wasn't for the network effect of my IRC communities, and Messenger groups, I could happily just use Discord tomorrow.
I strongly dislike that it's closed source and partly Chinese owned, but I've been using Messenger to reach people I couldn't on IRC for years already, and that experience is much worse, with no privacy gain.
Credit where credit is due, they knocked it out of the park in most aspects.
Also the protocol is open so it should be doable: https://mumble-protocol.readthedocs.io/en/latest/
For those curious about the switch from murmur to mumble in our conversation, murmur is the server side, while mumble is the client side.