Generally shotguns that aren't working right will manifest that with a much lower round count. It's usually right away. When a client shows up with a gun that isn't running right the first thing I do is try running my ammunition through it as fast as possible. Running the gun at my speed usually tells me where to start looking to determine what's up. Often we find that their ammo is not working right with their gun. (Very common...the ammunition should be the first suspect when a gun isn't running) If I attempt to run the gun and it isn't working properly it's usually either because the gun is new and something is wrong out of the box, or the gun is really, really old and hasn't been maintained. Police trade-in guns often show up to class where the new owner had no idea that the gun never saw any maintenance while in police use and it needs all the springs to be replaced, a new safety detent (on Mossbergs) or new shell stops, etc.
With a Benelli M4 you are most likely going to end up finding that problems running will come down to ammo. Benellis in general are pickier about ammunition than pump guns or the Beretta 1301.
On a pump gun, if the gun runs through a couple hundred shells of birdshot well and you run a few rounds of your preferred buckshot through it without issue, it's probably fine. With a semi-auto you want to be more careful in evaluating your buckshot loads, especially if they are "low recoil" loads that haven't been thoroughly proven in your chosen gun.
By that I mean that I've fired or seen fired many thousands of rounds of Federal Flight Control low recoil buckshot through 1301 shotguns without issue. I'd have no concerns about a 1301 running low recoil FFC buckshot if I picked up a new one tomorrow, so I wouldn't see the need to invest a bunch of money shooting FFC buckshot through the gun to verify function.
If you settle on Uncle Wuzzy's Ammo Haus' chained buckshot load as your preferred munition, I haven't a clue how that's going to run in a 1301 so you'd best test it thoroughly. Etc.
A 590A1 that's made right works just fine. I had a client a couple of weeks ago with a brand new 590A1 that ran like a raped ape. I've also had clients show up with 590A1's that had problems with the stamped parts that ended up locking up hard and had to go back to the factory to essentially be rebuilt.
A defensive shotgun needs to be reliable above all else. A properly built 870 or 590 will serve very well as a defensive shotgun. You will eventually break something on a pump gun, but it will take a while to make that happen and most people aren't using their guns enough to get there.
Round count depends on the class. Some of my classes have gone through nearly 300 shells in a day. Some have gone through a little more than 100. It depends on the clients in the class and what they're capable of. My Home Defense Shotgun class tends to be lower round count because people are usually drinking from the fire hose and they're not used to the sheer physicality of how I'm teaching them to run a shotgun. HDS runs every string of fire from a cruiser ready setup of the shotgun precisely because I only have people for a very limited amount of time and reps, so I need to ensure they master the most critical part of using a defensive shotgun: Getting it into action. A consequence of that is that they also get as many reps as possible setting the gun up for cruiser ready. This is especially important for people running semi-auto shotguns because each of them has their own unique control system that damn near nobody actually trains on enough.
In HDS I have to teach a bit about home defense, teach a bit about the nature of the threat, teach a bit about the realities of violent crime, teach a bit about how the police ain't showing up, teach a bit about how shotguns work, teach them how to live safely with the gun, teach them about justifiable use of force, and then teach them how to use the gun. And during lunch I try to teach them how not to get shot by responding police. The rest of the time is spent teaching them how to load, manipulate, and shoot the gun and a little bit about using cover. It's 50 pounds of material I'm trying to cram into whatever vessel a client brings to the class. Some folks show up with a dump truck. Some show up with a thimble.
The goal for that class is to prepare someone for the reality of home defense and to successfully articulate why they did what they did in the aftermath of using force.
My Shotgun Skills class presumes someone has already had all that and just goes into greater depth about actually performing with the gun so we start making loud noises after the safety/med brief and we shoot as much as possible. That class is about repetition with coaching...coaching being a rare thing to encounter in training, unfortunately.
No. Short stroking happens, but generally it's happening to people who have not ingrained the correct level of aggressiveness in running a pump gun. The only thing we do gently with a pump shotgun is press the trigger. Everything else is brute force, and as much of it as humanly possible. We have to run the action forcefully to the rear, and then forcefully forward. I run a pump gun with far more aggression now than I did when I first started hunting with one. In class believe it or not, I rarely see someone short stroke a pump gun. When I do it's usually because they are a smaller statured person with an ill-fitting gun. One of the reasons we want to get a shorter stock on a defensive pump is to allow the shooter to get as much muscle on the action as possible. I also take time in class to show folks that the next shell is only released from the magazine when the forend is at the absolute last amount of it's travel.
Focusing on running the action hard and literally showing them that the next shell doesn't pop out until the forend can't move anymore tends to accomplish the feat of taking people who are fairly unfamiliar with defensive shotguns and turning them into people who run the action harder than Ike was on Tina. They're usually pretty tired by the end of the day, but their guns run.
So I'm not super worried about people short stroking a pump gun once they've been introduced to the proper level of aggression with which to run one. When you run one like a viking berserker swinging an axe, short stroking stops becoming a problem. Then the only time I see it is if someone is trying to make me fall in love with how fast they can fire a followup shot with the pump. If they want to make me fall in love I give them the floor and let them try it a time or two, and invariably they make a mistake like short stroking and that's when I tell them that a fast click isn't nearly as impressive as a boom another tenth of a second later. The point gets made and they move on with their life.
The M4 is a fine shotgun. It's expensive, heavy, has a more limited aftermarket and tends to be pickier about ammunition than the Beretta 1301. That doesn't make it a bad or unreliable shotgun because it's not. Every M4 I've seen (not that there have been scores of them) fed with ammunition it likes runs great.
My personal choice is the Beretta 1301. I own two and I've seen literally hundreds more in class and I can count on one hand the number of problems I've seen with them. I'm about to have to start counting on the other hand because of an increase in issues from more recently produced shotguns I've encountered, but even then a lot of those are the result of some aftermarket parts that don't play well with the gun. (Aftermarket magazine followers, for example, are a terrible idea right now)
The Beretta is lighter, cheaper, and doesn't care much what you feed it. The only ammunition my guns haven't fed are beanbag rounds...and I don't expect it to feed those anyway.
I usually keep a 1301 staged for home defense. Lately because I've been too lazy to load my 1301 back up since they have been doing teaching duty, I've kept an 870 staged for home defense. I spend enough time behind both to not really care which one I'm using.
People often ask what the point of a pump gun is in a world where the 1301 exists.
Pump guns are still relevant defensive tools because I watch people who own 1301 shotguns come to class and for the first few reps stare blankly at their gun as they try to remember which button does what and what order they need to be pressed in. I don't have that problem because I shoot defensive shotguns far more than the typical person by exponential orders of magnitude. Most people are not training or practicing with defensive shotguns much
if at all.
I have a significant number of regular clients that treat coming to my class as their training and practice with the shotgun. That whole "recency" thing isn't something they've quite mastered yet. A good many of them have nowhere but the ranges I'm using that they can shoot anything but slugs...so it's understandable. I have clients that spend half the year in a country where they can't have so much as a pen knife, so ingraining skill is harder.
So if you are going to be the kind of person who does a class once or twice a year as your training with the defensive shotgun, you're likely best served with a pump gun.
If you're the kind of person who is going to spend 5 minutes a week on dryfire with your defensive shotgun, you go to the range once a month and work through a couple of boxes of ammo, and you take a class or two a year to use as a test of where you're at...well...you're probably just fine with a semi-auto.