We set up a bridge between the Lemmy.world General Matrix room and the Public-1 channel on the Lemmy World discord server yesterday. It's not perfect as emoji reactions aren't visible and some minor things like how it handles edited messages but other than that it seems to be working well.
Now people on both chat clients can interact with eachother!
I recommend fluffychat to most people because it's simple and straightforward. I use Element because it's fully featured and a bit more complex. So choose your poison
I would also recommend fluffy chat to people because in addition to that it's also one of the only ones to support multiple accounts, an important feature for element because simply switching back and forth between accounts isn't feasible on a service with end-to-end encryption where you have to maintain a single login else lose your keys and prior encrypted messaging history.
I've personally been using Element and love it. I have a private matrix server for my family to use. Some of the members of the family have also loved FluffyChat.
Since it's been mentioned here but nobody's said anything else about it yet, Beeper is nice because it connects a bunch of different apps and everything syncs instantly between PC and mobile. I personally use it for Matrix, a couple of Discord servers, Messenger (for those friends who won't leave) and SMS.
Only text channels I believe. There's a sidebar sort of like the one in the actual Discord app that shows your inbox, SMS, Messenger, etc. Discord servers show up in there, then when you select one it shows you the list of channels as though they're regular conversations. You can set whether or not they show up in your inbox and/or notify you individually for each channel, and the ones you don't want you just set to low priority and they'll be hidden. It's not a perfect replacement, but if you don't need voice/streaming it works fine.