Advantages of this are:
Faster (less CPU/Memory usage, less lag in games)
Discord uses 3 times the ram of TeamSpeak
Better voice quality
TeamSpeak sounds way better, maybe its because we can host it ourselves and choose a good host. Or just the fact it sounds better!
More integration with games we play
Like? See what users are playing???
Don't even have to download software if you don't want to, can be launched on browser.
Browser is buggy as hell, no PTT and voice delay.
Bots and other interesting things.
Just bots.... really. TeamSpeak has that.
I've used Discord for a while (5 months) and it's not for communities, more for small groups of people and streamers (they've made that clear). They're too cocky saying it's both a replacement for TeamSpeak and Skype. And remember people can make there own servers for free.
I'm sticking with TeamSpeak.