When you start a screen session, it will always copy the environment from your shell. When you start a second screen session, it will inherit a possibly different environment.
But tmux, on the other hand, spawns a tmux server when you first start a session. It'll copy the environment from your shell. However, from that point onwards, new sessions will use the environment from the server and will not copy the environment from your shell.
I like screen's behavior more. A frequent use case is to start a long-running command as a sort of ad-hoc background job. That's really easy with screen (just run screen and run your command, it will always use the parent shell's environment) but relatively easy to screw up with the environment when done with tmux. It kind of works only if you don't have a tmux server already running.