To be fair, I don't think you can't realistically compare the refereeing of such different sports. For one thing, the laws of American football are lot more tightly defined, with each player only allowed to do certain things, tackle in specific ways etc., so in theory at least there's less left down to the referee's discretion. And in the NFL there are six officials on the pitch each doing a specific job and watching for specific infringements, not just one guy in the middle and a couple of guys running up and down the side.
Even the NHL has four officials on the ice, and that's a much smaller playing area than a football pitch (yes it's a faster game, but the officials have ice skates on as well so they can move quicker too!)