What MattKing said. I use the same Jobo 1520 tank for B&W and E6, though I haven't done E6 in a while. I don't use soap, though I have been known to use the same water I wash my film in so there might be wetting agent in there.
Warm/hot water, plenty of rinses, a cheap toothbrush to get any residue out of nooks and crannies especially lids and light traps. You just want to be sure that there are no chemicals from one process still in the tank when you move over to the other process. The same really as what you'd do after fixing, but before developing your next B&W film...but just be a bit more thorough.
Don't use the dish washer unless you can dedicate a dish washer to photo equipment only...as they tend to keep a reservoir of water and recycle it...so you'd get low levels of photo chemicals on your dishes and glasses the next few runs. Not ideal especially with colour chemistry.