As a communication platform, I think that Discord is quite good. It allows people to chat and screen share very easily. The site itself is pretty self explanatory. Discord’s user interface looks like a cross between Skype and Slack. It's completely free to use, and is available as a web, mobile, and desktop application. Within Discord, users can create their own servers and host private, password protected, or public channels within those servers. It has many features, including a game mode for if you’re livestreaming so you don't show private information. It goes down to the "phone mode" very well and is responsive. It doesn't clutter your screen with information and designs. Overall easy to use.
I don't use teamspeak. I highly prefer Discord. TeamSpeak is a VoIP tool that allows groups to communicate using voice-chat in real-time. The server and client apps cost nothing and are freely available for download. They make money only on the service. You can use the TeamSpeak service for free if you don't intend to go beyond 32 users. You have to buy more slots which may not be people's favorite. The place to find this payment tier method is hard to find. Unlike Discord, it took me several minutes to look through the site. Participants pay nothing, but only have to download and install the app. The site is responsive as well. Even changing up it's design a bit. I'm not very fond of how the information is placed. It's a little hard to find things unlike Discord. where it's all there.