Matrix is a modern and decentralized protocol. It has the advantage to be simple to use, keep backlogs even when disconnected, and use the same account on any device. Furthermore, you can receive a digest of discussions by email if you don’t connect for a long time. Matrix has several clients, one of the most known and advanced is Riot, available on a wide range of platforms.
IRC is a legacy protocol, centralized and a little more complex.
You can access the discussion rooms (or discussions channels if you prefer IRC vocabulary) whether using IRC or Matrix. Each protocol can be used through several clients: Riot, Quaternion, Nhekho etc. for Matrix, Konversation, Quassel, Xchat, Thunderbird etc. for IRC.
If you are hesitating between the two protocols, you may certainly want to go with Matrix. Please follow this quick guide to create a account.
Important notice: If you prefer to use IRC, due to important spam in Freenode servers, where we are hosted, please register and identify your nicknames to NickServ, or you will not be able to talk.