Nuclear power is steam power, the radiation heats the water and the steam generates the power.
Steam punk nuclear would have the steam from the nuclear reactor being pumped throughout the ship and directly running pistons that operated mechanical devices like elevators or large blast doors. Factories used to operate that way. It could be considered more efficient, you loose energy converting steam pressure into electricity, and then converting again into physical force. The efficiency makes more difference if you are operating heavy machinery like mining equipement or heavy presses, rollers, etc.
Engines could just be steam further superheated into plasma exhaust.
Another cool concept might be some kind of warp field FTL drive where steam powered pistons keep some kind of device spinning generating a powerful field, similar to an electro magnet.
This is where the concept gets interesting, if our warp field does something to screw up electrical equipement, which is why our ship uses fully steam driven mechanical parts and manual switches.
What I'm describing has nothing really to do with Firefly, but it's a fun concept to play with.