What football are you watching that goes straight into a shootout? They play an extra 30 minutes of ET.
It's a lot easier for hockey players to keep going for hours on end because they have intervals of 30-45 second shifts and sit for a good two to three minutes (+ TV timeouts, face offs, period breaks.), soccer players run for a full 90 minutes with a break at half then an extra 30 if need be on top of that.
I would argue that hockey players work just as hard as a footballer, maybe even harder in more frequent shorter bursts, which will make a much bigger strain on the body. It is full contact and never a chance to let up.
They also play back to back, or 3 to 4 times a week. Footballer work at a steadier level across a longer period of time, with moments of extra exerted energy.
Footballers are actually only playing for around 40-50 minutes of the 90* (because of the continuous clock, even with the ball out of play, or stopped for a free kick, etc) with maybe a portion of that spent at full tilt. Because of the nature of football (and the size of the pitch) players can slow down for moments and be away from the play, taking up a position and then getting back into it.
In hockey the team play for a FULL 60 minutes, as the clock stops for breaks in play. Also because of the way the sport is played, players are generally involved for an entire shift and never have a chance to step away from the play (unless you are Henrik Zetterberg during the regular season) while on a shift.
I am not knocking football as it requires a lot of effort and skill, but to insinuate that it is 'easier' for hockey players is way off in my opinion. Both sports will see the players come off at the final absoultely fucked, if they put in the right amount of effort.
I would love rule changes to both sports when it comes to Overtime:
NHL: 3 on 3 - 5 minutes, then 2 on 2 until a goal is scored
Football: 7 on 7 during extra time for 2 x 20 minute halves.
Opening up the area the sport is played in, should in theory create more openings for scoring opportunities, thus negating the need for a shootout of any kind.
*Wish I could find the article that showed this.