The payouts for each of the wheel variations are exactly the same, but the odds are not because the American wheel has the extra pocket. See the roulette odds page for more detail.
The European wheel has 37 pockets, including numbers one through to 36, and just a single green zero.
The American wheel has 38 pockets, including numbers one through to 36, the single zero, and the 00. Although you could argue on the American 00 wheel, at around 00 there is a slightly higher average of red pockets, and at around single zero, there is a slightly higher average of black pockets. The most obvious is the alternation of red and black pockets because they do not represent any specific sector of the wheel.
The roulette wheel layout and the roulette table layout are a deliberate randomisation. As a professional roulette player, the first and most critical thing to understand is that there is a big difference between the roulette table and the wheel.
