Yeah, not really a very answerable question. In terms of physical toughness, stamina, and skill, the sports have quite different requirements.
Like some other predominantly North American sports–baseball, for instance–American football is a far more specialized game than rugby. Each position, with a few exceptions, has a much more tightly circumscribed set of roles in American football. If you’re on the offensive team, chances are you’ll hardly ever have to tackle a guy who’s carrying the ball. Conversely, if you’re a defensive lineman, you might go a whole season without ever getting your hands on the ball during a game.
In rugby, by contrast, everyone gets to carry the ball at some stage, and everyone has to make tackles. Not only that, but the kicker–gasp, shock, horror–actually has to be a player on the team, not some guy who gets brought on for ten seconds when a field goal or an extra point is needed.
American football can have huge, 300+ pound guys on the field because these guys are required to do only a limited amount of running. Such big guys probably–strike that, definitely–couldn’t keep up with the pace of play in a typical rugby match. With the exception of a few props, the biggest rugby players tend to be leaner, lighter, and faster than the biggest NFL players. The constant stop-start of an American football game, with all the time-outs and changeovers, makes even the slowest rugby match look lightning-fast by comparison.
The different rules about hitting in each sport also leads to different types of skills. As others have noted, if you don’t have the ball in rugby, you generally don’t have to worry about being hit. This is not the case in the NFL, and knowing where all the safeties and corners are, and being able to get clear of them, is a key skill for a wide receiver. The ability to leap and take amazing catches, as many NFL receivers do, is also something not seen very much in rugby.
In rugby, on the other hand, a key skill is the ability to create gaps and overlaps through speed, power and strategy, because the ball can only be thrown backwards. Also, because the ball remains “live” even after a tackle has been effected, there is considerable skill involved in keeping the ball in the hands of your team. Kicking in general play is also an important skill in rugby.
From a strategic viewpoint, rugby is also considerably more spontaneous that American football. While the coaches in rugby might plan an overall strategy, and send out messages onto the field during a game, they do not make the play-by-play calls in the same way that NFL coaches do. The idea of the scrum half or fly half listening to a sideline coach before every scrum or lineout for a play call is totally foreign to rugby.