Why didn't Naruto's Rasengan beat Sasuke's Chidori?
The standard Rasengan has no natures associated with it.  It was originally based on the Tailed Beast Ball, which is simply a dense amount of chakra directed at a target.

Eventually, Naruto adds his wind nature to Rasengan, which, in turn, creates several different variations of it.  But neither of these variations are being discussed.



However, this doesn't mean that either Chidori or Rasengan have a direct type-advantage over the other.  At that point, it becomes a matter of the abilities and strengths of the wielder, and as we now understand it...


   ...it ended in what could be seen as a draw, with both Naruto and Sasuke losing the arms in which they perform the jutsu for their final fight.