I have found that the number of players does not matter but rather the players themselves. In a six player game, well in all games below 7 players, resistance members have to make perfect choices on missions 3 and 5. What that means is that the players with the spy role are doing something to tip off to everyone that they are spies which makes them easy to not put on a team.
If you look at the simple math for missions 3 and 5 you will find that the resistance has gathered a lot of information if they can keep picking perfect teams. With a resistance member as the team leader on the first pick they have a 60% chance of picking right (assuming they pick themselves first), 3 resistance 2 spies. Each pick they make lowers the odds pick 2 takes it to 50%, 2 resistance and 2 spies. Pick 3 takes it to 33%, 1 resistance and 2 spies.
How often each side wins will boil down to the play style of the group playing and how much unintended information they give out. Truth be said from my experience playing this at all player levels the spies should have the edge and win more often because they have perfect knowledge in the game and the resistance has flawed information.
Also are you playing with any of the expansions?