[iFrame]

Let's take a close look at both:

Teamspeak:
Chatting: not so good.
Voice: really good.
Managing a server: not an easy task
Hassle to host one: also not very easy, you've to pay too

Discord:
Chatting: really awesome
Voice: really good
Managing the server: very easy
Hosting the server: child's play and also it is free.

Here we are with the results, Discord is the clear winner and majority seems to agree with that too