Okay, so #Matrix: positives are that the #Riot client has a beauteous interface; Matrix.org's bridge to #Freenode offers ever-growing scrollback in #IRC rooms; possible to !selfhost a matrix server. Minuses: I haven't yet found a matrix.org bridge to #XMPP (which would greatly enhance its value to me); no concept of individual conversations, just rooms with limited membership; rooms appear to be permanent unless manually destroyed by their creators/administrators before they ever leave the room; project is very dependent on a single company's sponsorship, so subject to the fortunes and management of said company.
I do like Matrix, at least as I experience it when using Riot on Android.