I find the concept of droids such as Artoo and Threepio having personality, emotions and some level of intelligence really interesting, when they are pretty much considered slaves/servants with masters. See also Is C-3PO a slave?.
Artoo flew with Vader to Mustafar, while C-3PO travelled there with Padme. I think if Vader had beaten Obi-Wan, and claimed ownership of the droids, they might have tried to escape out of allegiance to Padme, but let's pretend up until this point they were both considered Anakin's property, moreso than Padme's.
Would they have willingly accepted Vader as their master and helped him wipe out the Jedi and rebellion (if they had any use), or do they have some sort of moral compass and would have tried to escape or foil the empire's plans?