It can depend upon how bad the scripts are written on some servers for the clientside mission files, e.g. performing pointless checks every frame, when they can be done say once per second.
There tends to be a lot of these threads checking every frame.
The FPS will be better in single player (unless it's a custom scripted single player) as less scripts running.
Not really much you can do yourself online. It depends if someone's taken it upon themself to optimise a mission's scripts further for their server playerbase.