It depends on how you play. I mean, I play low level inline hockey, so make of it what you will, but I actually prefer the off side. As a right handed defenseman, I like my hips to be open to the play. I have so many more options since I can see everything to my right, but I can still send a bank pass off the boards to the forwards if need be. I get tunnel vision when I play the 'correct' or 'natural' side. I can see the wall, and I have to look over to pass or shoot, and when it comes to shooting, I have very little options. On the off side, I can pull it around the goalie to the right, I can deke left and get under my stick for the backhand, or I can simply shoot and pick any corner I wish. On the right side, it's throw at the goalie and hope he's off his angle.
Then again, I also use a near flat stick, and I'm pretty good at passing, receiving passes, and shooting off my backhand. But it can be really difficult for most people, even professional hockey players. Playing on the 'natural' side gives you more direction, you generally have an easier time knowing exactly which play is the right play, instead of having to choose from a number of options and hoping for the best. It's also easier to receive a pass in stride, especially when you have to worry about receiving passes at the blueline. Sometimes if someone passes to your stick and your trying to get onsides in the offensive zone it's easier for the defender to pinch against you and prevent you from entering. At least that's what I've noticed from my amateur experience.