I'd say Discord. Doesn't matter how much packets of data it uses, it's far better than Teamspeak. Of course this isn't to demean anyone, I respect everyone's opinion here and these are my personal views.
Coming back to the comparison, I think it's Discord that's much more feature-rich and responsive compared to Teamspeak. Responsive in the sense, it easily integrates with bots without much hassle. That's a plus point of it. Also, all other features are appealing starting from profile to badges (of course you gotta buy nitro for this), even the skins and overall appearance.
At HelioHost, we operate a full-fledged support channel on Discord. There's also the News channel along with the support one. A lot of people find it easier to write to us on Discord rather than making a post on the forum. Best part is, they find someone or the other online to get their problem immediately solved or at least assure them that their concern will be taken care of as soon as a root administrator is online. Mostly we have general chat in the channel, although essentially meant for support, mainly bcuz Discord isn't still a very popular choice in terms of availing support and the majority aren't aware of it being a feasible option, to be honest.
Anyways, these are few reasons why I prefer Discord and that makes it a personal favorite. Nevertheless, I also should say that Teamspeak has its own plus points, which is the reason why it exists and still competes with Discord. TBH, I used it only on one occasion, that too it was too brief a use that I couldn't explore all of its features, and that's one reason why I didn't comment much about it