screen is one of those things that's been on my todo list for way too long, along with its alternatives(?), tmux and byobu. Anyone that uses/used all three and can offer a comparison?
byobu is something like a theme or packaged config for screen, so it doesn't really need to be treated separately.
The biggest difference between tmux and screen is that tmux is a lot more flexible with regard to laying out groups of sub-terminals within the main terminal. screen is mostly limited to one-at-a-time, horizontal splitting or (in very recent versions) vertical splitting, while tmux lets you go nuts: http://tmux.sourceforge.net/tmux3.png
Also, GNU screen is very old and stable, while tmux is (so far) still new and flexible. For example, tmux very quickly added support for handling Unicode characters beyond U+FFFF, a feat that (so far as I know) screen still can't manage. That's only one example, but I'm sure there'll be more as time goes on.
EDIT: One other thing that tmux does that makes it better than screen: when I start up a tmux session from within an X11 session, tmux clears the $DISPLAY variable so that processes running inside tmux don't try to connect to the original X server - which may very well have gone away at that point. It's a small thing, but incredibly annoying when it happens.
I switched from screen to tmux a while back. The key thing for me is that configuration and manipulations/operations in general are more user-friendly. Otherwise, in terms of the basic use cases, they are essentially the same.
I have used screen for many years and decided to finally give tmux a try about 2 months ago. I really enjoy it. It took some adjusting, but overall I like it better.
Things like this are largely due to personal preferences, though. All I can tell you is that I am happier with tmux than I was with screen. It is more modern, and the split screening capabilities are better.
I switched from screen to tmux about three months ago. It's easier to configure, does vertical splits, and is under more active development (apparently).
