I actually don't mind watching American football....however, I realise that it is TOTALLY different and unique and cannot be compared or contrasted with rugby league. But, since you asked for it, here is a comparison:
Duration of Game
NRL - 2 x 40 minute periods of play, with timeoff blown only at the discretion of the referee
NFL - 4 x 15 minute periods of play, with the clock stopping whenever the ball is made dead (incomplete pass or taken out of bounds). 40 second play clock. Coaches have three timeouts each per half
Teams
NRL - 13 players on field, 4 reserves. All players can pass, run and kick the ball.
NFL - 55 players in each squad, 11 on field at any one time. On offense, only six players can make a play with the ball. The quarterback passes or runs with the ball, the halfback and fullback run with the ball, the halfback, fullback, wide receivers and tight ends receive the ball from the quarterback. Defenders consist of defensive ends, defensive tackles, linebackers, cornerbacks and safeties. Kicking and punting are specialist positions.
Gameplay
NRL - Continuous action, 6 tackle sets (99% of time teams kick on fifth tackle). Ball can only be passed backwards. Objective of game is to score a try, which is scored by placing the ball on the grass in the 'in-goal' area, which is followed by a conversion which is taken in line with where the ball was placed on the ground.
NFL - One play taken every forty seconds. Objective of game is to advance the ball ten yards within four downs (tackles/plays). (99% of time teams punt/kick on fourth down). When the team has passed the ten yard line, they are given a new set of downs ('first down'). The game continues as such until teams score or turn the ball over (through either fumbling or intercepting the ball, or failing to 'convert' a fourth down). Touchdowns are scored when the player carries the ball into the ingoal area, which is followed by a 'point-after-touchdown' attempt which is always taken straight in front of the sticks. Field goals (three points) can be attempted at any time, most commonly on fourth down.
Off the Field
NRL - 15 teams competiting in one big happy league, teams play 24 games as well as finals, State of Origin and Test matches. Each team has one coach, at least one reserve grade side, and extensive junior recruiting systems.
NFL - 32 teams competiting in two conferences of four divisions each. Teams play 16 games, and elimination finals, as well as a 'Pro Bowl' game. Each team has one head coach, one offensive co-ordinator, one defensive co-ordinator, one special teams co-ordinator (to teach the gumbies how to kick), and a specialist coach for each and every position (quarterback, halfback, fullback, wide receiver, tight end, offensive tackle, offensive guard, centre, defensive tackle, defensive end, left linebacker, middle linebacker, right linebacker, cornerback, free safety, strong safety, kicker, punter). Players are recruited from college football through the NFL draft, with the rejects playing either Arena Football, NFL Europe or (sorry Canadian Steve) in the Canadian Football League.
The Average Player
NRL - Each player MUST know how to tackle and pass the ball. At least three players in each team also has a good knowledge of tactical kicking. Every player is multi-skilled - props can offload and pass, wingers can be great physical defenders. The same 13 players on the field must attack and defend, and do not rest except during scoring breaks and halftime. Some may say this demonstrates the defiencies of rugby league players; on the contary, it illustrates how versatile the atheletes who play the game really are.
NFL - The vast, vast, vast majority of players can only perform at their nominated position. Quarterbacks do NOT and CANNOT play defensive end. Linebackers do NOT and CANNOT play halfback. Kickers do NOT and CANNOT play offensive guard. As demonstrated before, the success of the offensive side of the ball can be totally independent of how the defense is operating. There are virtually two different teams within each franchise (three if you count the kickers).
I hope I have covered everything. Two totally different games.