Well, perhaps Darth Vader would recognize R2 from his past with Anakin. He might initially be hostile but then start to have memories resurface. This could lead to an internal conflict within Vader as he battles between his current Sith self and the remnants of his former self that had a connection to R2.
One possibility is that Vader tries to use R2 to gain an advantage over the Rebellion. He might think that R2 has valuable information about their plans. But R2 being the resourceful droid it is, could outwit Vader and escape, or even plant false information in Vader's mind if it has the right hacking capabilities.