The initial release of tmux was in 2007. The initial release of screen was in 1987. I assume they don't update as frequently because it's relatively stable.
I use screen because tmux forces me to explicitly define quick bindings for each binding where I don't want to lift my finger before pressing the letter. So, where I can write `C-a c` in screen without taking my finger off the keyboard, I have to explicitly add `bind-key C-c new-window` in tmux.conf for this. Otherwise it's not as ergonomic as in screen, and now I have to do configure this for each key I use, which granted isn't that many, but still it's a nuisance without a good justification. Tmux is fine for me if I ignore that. But some people miss certain screen features in tmux, so it's fair to mention that as well.
The above is how most people first configure tmux, since C-b is just awkward. `bind-key C-a send-prefix` is optional of course, but is used to forward C-a to the active window (beginning-of-line in shell and emacs). How would you do that in screen?
The default for `previous-window` is `prefix-p`. Run `tmux list-keys` to see all active bindings.
The only real downsites are if you use screen/minicom/etc inside tmux you tend to mash Ctrl-a quite a lot, but if anything that's easier than keeping track of which key goes with which level?
(I mostly hear about this stuff because I still used screen and tons of people are like "why don't you tmux")