The real difference is the intensity of the impact.
In boxing you are hit by a single padded hand. The boxers muscles are mostly to accelerate your hand and glove up to speed and to follow through, but little is applied during the actual punch due to rebound.
Kinetic Energy = (1/2)(Mass)(Velocity2).
A strong punch is about 9m/s which is about 20mph. A hand with glove weighs less than a pound including the hand. A linebacker weighs about 250 pounds and is moving at about half that speed at impact. So even at 1/4 the KE per pound, he still delivers 62.5 times as much energy.
Add to that the difference between padded glove and movable head vs hard helmet to hard helmet locked in a neck brace and you see how football causes heads to undergo a much higher energy dump.
Punch speed data from the abstract of http://bjsm.bmj.com/content/39/10/710.full
– GooberMcNutly