Byobu had a bug where logging in to a heavily-loaded server would spawn infinite apt-check processes. At the time of writing, the fix is still in the process of being pushed out to Ubuntu 12.04 LTS. If you manage other operating systems, you'd want to check their package version/bug trackers as well.
The default display also includes the time in seconds, so sending updates continuously when it doesn't need to. (Annoying network traffic, possible side-effects in the client terminal).
If you disable those, it's nice and pretty. It's easy to change the configuration for your user, using the byobu-config frontend. I like that it automatically enables ctrl-a in tmux (plain tmux uses ctrl-b). And unlike tmux,
byobu with no options will conveniently create a new session if there isn't one, or attache to the existing un-named session. I'm happily using it at home.
For deploying to a number of different servers, possibly managed by multiple people, I'd consider whether plain tmux might be safer.