I have rifles in small fast and big slow calibers, the whole one pushes and one kicks thing is sort of true... but its not just a push. Big calibers are going to move you, they are going to kick back hard, and the recoil energy is not going to be sucked up by your body fast. This is where the "push" idea came from. When I first shot my .458, a family friend looked at me after the gun made me move back, and told me he wasn't going to shoot it, especially if it moved a big guy like me.
So the gun does kick back hard, but what you remember is the feeling of the gun pushing back on your whole body.
Smaller faster calibers are going to come back fast, but they dont have the same recoil energy, so your shoulder is going to take it, and not so much your body, so your shoulder is all you are really thinking about.
It seems to me that it is all about perception. Shooting my .458 "all day" gets up to about 10-15 shots before it gets too hard and too expensive. If I'm out shooting the -06 all day, that might be 50 shots. If I'm shooting milsurp, that could be in the hundreds of rounds, making for a very sore shoulder, and you start to think it's slapping quicker every round.
So what I say is the smaller rounds kick, and the larger ones kick and push, making the push more noticeable.
If you have a big gun weight wise, in a big caliber, it is going to slow down the recoil velocity while keeping the total energy, in this sense, it is going to be more of a push.
If you take two guns at the same weight one in a larger caliber, it is going to come back faster and harder.
If the big bore is truly a bigger gun, and it comes back slower with the same amount of energy, it is still going to carry inertia (the gun will keep moving, against the resistance of the body)