Discord is simple to use, organize, and join as well as being easy on the eyes. Users in the discord can easily communicate through different text channels or if they so choose, voice. It also makes for easy switching between servers and communicating directly to specific people in private messages.
Now, I have limited experience with TeamSpeak, but from what I remember it’s mostly a good voice communication program and isn’t really great for messaging and honestly, it feels outdated. All of this is opinion, but Discord stuck with me, Teamspeak (and mumble) never did.