Caro-Kann or Petrov/Petroff?

If black doesn't want to lose, which one should he/she pick? Which opening is more drawish/defensive?

The petrov has a very drawish reputation, while i've more often heard the caro kann described as solid.

So the Petrov/Petroff requires more theory than Caro-Kann? Which one is more positional?

No one wants to lose. But do you want to win? Who's afraid of an e-pawn?

Caro-kann to the end

I'll go ahead and say that Russian needs less theory than caro kann. Could be completely wrong though

Neither is solid, if white does not want a quick draw.

The Nimzowitsch-attack can lead to a pretty violent game against the Petroff. At least on amateur level one might even face the Cochrane-Gambit from time to time.

Caro-Kann advance variantion is very sharp and even the old main variation is not an easy draw for anyone below GM-level, as the resulting endgames are quite complicated.

If there was a best drawing weapon, everyone would use it. On amateur level, one might even be better off with for example modern Philidor (early exd4) than Petroff. 

Other options are of course Berlin-Defense or Schliemann-Gambit, which can both lead to drawish queenless midgames or endgames quickly.
But always remember: An easy draw between topengines and professionals is still plenty of play between patzers. (Patzer defined as anyone without at least IM title)