I don't do ANYTHING all the time so I'll have to say both ... I've case skinned many a beaver ... works great and once ya get your mojo rhythm thingy going you kinda slip into autopilot mode

prep all ya plan to skin at one time (remove feet, cut around tail, make your opening cut from base of tail up to just above the vent ... keeping it as short as possible but manageable ... then start skinning what you got open ... you'll decide whether you prefer to pop out the legs on the bench or once hung ... I hang mine by the tail using a loop of heavy braided small diameter cord, using the loop I make a slip knot by passing one end back through the loop ... then hoist to a hook secured to a rafter or whatever solid beam ya got ... I like mine to hang fairly low ... that's just another preference thing you'll figure out on your own if ya give this method a try
If I'm fleshing a beaver I very much prefer it to be cased ... a lot easier when working it on the beam