As mentioned, the house edge and odds for European Roulette are better for the player, compared to American Roulette. The house edge is a lot lower at 2.7%, and the odds of winning by betting on specific numbers is 1 in 37.
American Roulette: In American Roulette, there are two green zero pockets. This means that there is an additional chance that your wagers will be void. It has a payout of 35/1 if you bet on it, but it essentially doubles the likelihood that all bets will lose money.