Pumps do produce more felt recoil than semi's but the inertia operated Benelli is pretty stiff and the stock design of both the older Benelli (pre-Super 90) and the Beretta will make many shooters think they are firing a torture machine. Gas operated autos deliver less felt recoil than either, but are generally not bet-your-life reliable with heavy buckshot/slug loads. I have exactly NO experience with the new M4 Benellis, so cannot comment about them...except to say their price is unfreakingbelievable!
While it is not possible to undo the laws of physics, there are several ways to manipulate them with heavy loads in shotguns. Gas operated guns do this by "spreading out" the recoil via a longer, less abrupt, method of operation. Inertia/recoil operated guns do it via a series of springs, and pumps don't use any mechanical methods at all. One little "secret" with pumps is to be certain the headspace is tight. When we used to do demos with issue 870's you always picked a gun with a tight bolt lockup. (which is the only quick way to gauge headspace on a range and is NOT accurate for real measurement purposes)Believe it...a gun with loose bolt lockup will get a "running start" on recoil and thump you noticably harder.
Things like stock fit...a too long stock will kick your ass!...and design...no high, sharp combs a la the older Benelli's...are important in minimizing felt recoil. Imagine the butt of a shotgun stock...basically a 2x4 with rounded edges and a little pad, maybe. Take a 2x4 and hold it a couple inches away from your buddy's shoulder, then smack the end hard...hurts, no? Now try it with the end held hard against the shoulder...all he will feel is a hard shove...much more comfortable. Hug that shotgun tight! For me, at least, a pistol grip on a stock seems to increase recoil, not to mention getting in the way if you need to do anything more than shoot from a static position. Stockless pistol grip guns are a joke...a bad one. Things like gee-whiz recoil reducers usually fail under any sort of hard use and cost way more than they are worth.
Spend some time at a range with several different standard type shotguns and I'm willing to bet you will find one that works fine for you with effective ammo without all the voodoo gimmicks.