Although I generally prefer open source solutions and protocols, which would push me towards RocketChat, I think that Discord would place a lower burden on us to manage the thing. As @wjwwood says, I prefer to avoid self-hosting because we have enough to do as it is. Discord does “just work” and the tools are good.
Instantaneous chat with the ability to rapidly fire up a voice or video connection is far more important to me than integration with existing software development tools. If gitter can do those as well as integrate with GitHub, then great, but if it can’t then I say go for Discord or RocketChat.