Just thinking... the office server here has been in three different Antec cases, my gaming box has been in 2 Antecs and a Silverstone case. Same precautions as a new-build / upgrade - static management and patience are the only requirements.
The only gotcha I'd suggest (and it's nothing like as big a problem these days) on transferring everything to a new case is to make sure the mobo-mounts all line up and you don't have any pre-installed in the case that don't line up with mounting holes. Everything else is just time and patience.