Meaning that whatever messages you send, they will store and create a profile of you to sell to advertisers. It's been done before and is a very lucrative business. Even though on social media they say they don't, their EULA explicitly states in plain text that they're allowed to.
2. Deeper control
When it comes to control and customization, Discord is child's play compared to the other options. Teamspeak has a nearly multi-page long list of permissions which you can grant/revoke from users. Discord, while much prettier, offers a much more limited set of options.
3. Locally Hosted
Teamspeak is owned and hosted by the server owner, unlike Discord. This means that while Discord may have server issues (which they do, a lot), if done correctly the Teamspeak servers you're speaking of won't.