A question that often comes up in conversation is "Who would win in a fight?" This question applies in all sorts of fields: Ronald McDonald vs The Colonel, Blur vs Oasis, Tony Blair vs The Blair Witch Project and now...
R2D2 vs Daleks
Both are capable of extreme space travel, both are plucky adversaries and both are fairly hardy.
It is worth noting that one of the old tricks that used to work against Daleks, no longer applies. It was once said that to escape the Daleks, one simply needed to run up stairs. This was famously parodied in the latest series when Rose Tyler (Billie Piper) ran up some stairs and the Dalek used jets to hover. However assuming you have a Dalek without this ability, the benefit is negated anyway because R2D2 can not climb stairs either. So the venue for the battle is a flat surface.
R2D2 is esentially a dustbin with a projection unit and a universal lock reader. The Daleks are battle robots piloted by sentinent globs; equipped with laser cannons. R2D2 if it came up to you would make a Puruupuruu-twee-doot noise but the Daleks would yell EXTERMINATE and try to blow you to ions. Clearly Daleks are more menacing.I am reminded that C3PO and R2D2 once appeared on Sesame Street and R2D2 fell in love with a fire hydrant; clearly this is a weakness as the Daleks do not have love. Rose Tyler killed one when it experienced happiness. I'm not sure how this aspect would turn out.
A Dalek is taller and heavier, so in a one on one ram-raid, the Dalek would win. R2D2 frequently shut down and required repairs; I'm sure Davros would just send more Daleks. Collectively the Daleks conquered worlds, but R2D2 is merely a service droid.
In conclusion, a Dalek would beat R2D2 and for one other important reason... they killed Kennedy during their invasion of Earth in 1963 and overran London.