I could provide one. Though they're all ancient because I haven't played SS13 in quite a while due to switching my internet provider.
It depends on the players, game mode, and admins on how serious things are. I know one time we had Mortal Kombat style tournaments in an arena we built (used to be an admin).
Most of the time seriousness is created by the players. One particular case I can remember was as security, my HoS demanded I holster my weapon. This of course made me more vulnerable to enemies, but it prevented accidents and added to the "Role Playing" experience.
Overall, I'd say RP is 'common sense'. You're not superman, or a Christian terrorist, you're just an average engineer maintaining the engine. With that base, you can then make yourself interesting. Perhaps you used to work on a large battlecruiser, and often complain about the working conditions on SS13. Perhaps you're a captain, who is traumatized by his violent past. Perhaps you're an old janitor, with a story to tell if someone lends an ear. That's the kind of gameplay I think B12 aims for, not mass murdering and blood splattered walls, but interesting roll playing experiences that will stay with you for a long time.
Of course, this could have easily changed in the last 6 or so month I haven't played. Plus, not trying to put down the other servers, each strives to create a certain kind of gaming experience.