Another way to think of impulse is the force felt over a certain period of time, which is the same as the change in momentum.
An easy way to visualize this is if you picture a car accident. Old cars that were solid steel went from 30mph to 0mph in a very short amount of time when they crashed. The car going from 30 to 0 has a certain amount of momentum associated with it, and the shorter the amount of time in which that momentum change takes place, the great the amount of force felt. This means that you felt a great amount of force across your shoulder and lap from your seat belt. Newer cars are designed with crumple zones, which are there to maximize the amount of time that it takes the car to go from 30mph to 0mph, and when you increase the amount of time, you decrease the felt force on your body from your seat belt. The change in momentum is the same, as long as the cars weigh the same, since they're both going from 30 to 0 mph, but the newer car takes longer to come to a complete stop.
The same applies to your shoulder, given a constant recoil pad size, in that the less time it takes for the the rifle to reach its maximum recoil velocity, the greater the force you feel.
