I used the shotguns in AW more than any other weapon category. If you were to ask me what I thought about the balance within the shotgun class and in the spectrum of AW weapons as a whole, I'd say that they are quite well balanced for the most part. That being said, let's go in descending order, from least favourite to favourite shotgun.
In general, I like the variant balance on the shotguns (apart from the Bulldog Berserker). You could go for more pellets, tighter pellet spread, quicker sprintout, and even quicker movement speed. These are all very important on a shotgun, but unfortunately, you can't boost them all at once, so a lot of variants in this class have some merit to them.
I hated this shotgun. It is essentially a fully automatic shotgun that fires at 120 RPM, has the largest magazine capacity in its class, and has similar strength per shot to the Tac-19. Sounds great, right? Well, there's one massive catch: like a lot of weapons in AW, the CEL-3 Cauterizer's fire rate ramps up, like how the Bal-27 fires the first three bullets at a reduced fire rate. Well, the CEL-3 Cauterizer fires its first bullet at 60 RPM. Ow. That alone makes the weapon very sluggish initially, and to me, undermines any fire rate advantage this weapon has. To me, you have to either use it like a slower firing Tac-19 or a very poor man's USAS-12. I would've made it fire at a constant 120 RPM while having an even shorter range than usual (it does have a somewhat reduced range compared to the Tac-19) so that we don't have another USAS-12 case.
I don't care if this weapon is technically good for nothing, it's fucking hilarious. In 2060, we're still using weapons men in the 1500s were using, and it is an impractical but badass weapon. Although it has the range of the Tac-19, it has double the pellet count per shot at eighteen pellets over a huge radius. Unfortunately, the Blunderbuss' pellet per hip-fire spread ratio was equal to the Tac-19, so it wasn't that much more useful than the Tac-19. Really putting the nail in the coffin for the Blunderbuss was that it was a 13 RPM, single shot weapon. That being said, it is super satisfying to unleash the mountain of pellets upon your enemies. It also helps that I quickly got access to the Culverin, one of the best variants for the Blunderbuss that increases the pellets per shot to twenty and tightening hip-fire spread by ten percent, at the expense of a longer sprintout time.
This weapon is fucking hilarious in Hardcore due to the pellet being an instant kill if it lands, and you fire eighteen of them over a large area. Damn.
Ohm shotgun mode
I'm going to lump this in here, because I do have dedicated shotgun classes to the Ohm. It is one of the most unique shotguns you'll ever see. It's slow-moving, it has a colossal forty round magazine, it has shit damage per shot, can use Rapid Fire, and is overall hilarious to use. I don't like how the Ohm automatically switches back to LMG mode after dying, but that's another aspect of the Ohm that I should mention: you have a decent LMG at your disposal as well! The LMG mode is what's affected by the variants. As far as I know, the shotgun mode is not affected by variants in any way, but the LMG mode sure is. The Ohm is a hilarious weapon to use as a almost completely dedicated shotgun. Think of the old S-12 but with slower movement speed, five times the magazine capacity and ammo loadout, and the rapid fire attachment at its disposal. It's a super weird but beautiful creation in my opinion.
It may be at the middle of the road of my shotgun opinions, but I think quite highly of the Bulldog. This was the lone shotgun from the original three that was never modified, and as a result, it became somewhat obscure due to the massive S-12 buff and good Tac-19 buff. It provides a balance of accuracy, power, and fire rate in a package that is competitive, usually needing two shots to kill but you can get one with some luck. It also has one of the most beneficial variants in the game in the form of the Face Hammer, increasing the pellets per shot to nine and tightening hip-fire spread by twenty percent at the expense of not being able to use optical attachments (oh no) and a longer sprintout time. I use the Bulldog quite a bit when I want to take shotguns seriously.
This is a big favourite of mine in the scope of the shotgun category. Due to some great variants and a timely buff, the Tac-19 has quite a bit to offer in the form of reliable damage, bringing good pellet damage to the table like the Blunderbuss but having pellet spread akin to the Bulldog. The Tac-19 was quite a well balanced shotgun that made one shot kills quite satisfying thanks to its completely visual effect of an energy wave when shooting. It has a shit ton of fun and useful variants to use. You could use the Sledgehammer for more accuracy and a larger magazine, use the Upper Cut for quite an impressive pellet to spread ratio, use the Bang Stick for a fast-moving, fast-reacting shotgun, or beef up the range of the Tac-19 with the Round-House. There's a lot of ways to tailor suit the Tac-19 to your needs, and with it being a well balanced shotgun, I find it quite likeable.
If you like Gung Ho, your hip-fire spread won't go to complete shit with this shotgun, but the hip-fire spread is still too large for my liking.
This weapon has had a wild history. Before the March buff, the S-12 was the laughing stock of the shotgun category, firing at the same speed as the maximum Bulldog firecap while having the weakest damage per pellet and largest pellet spread of all the shotguns (before the Blunderbuss was introduced). Then, in one patch, the S-12's fire rate exploded from 469 RPM to 600 RPM and the damage per pellet was increased, still worst in-class but not by as severe of a margin anymore. These turned the S-12 from laughing stock to dominant shotgun. Until this game, a fully automatic shotgun with a fire rate over 500 RPM was never seen before, and the S-12 left its mark on the AW metagame. It flung buckshot so fast that nobody gave a shit about the poor damage per shot, since you could usually land five shots in the span the Tac-19 could land one. The fire rate was so high that recoil usually maxed out by the third shot, and the S-12 became the first shotgun to have problematic recoil. You could even turn its fire rate strength up to eleven as it has a lot of variants that fire faster, with the Tiger Blood taking the fire rate all the way up to 750 RPM, beating a few SMGs in that regard. Yes, you read that right: a shotgun firing faster than an SMG and most assault rifles.
For the most part, the Whirlwind was the dominant variant in terms of popularity. Although suffering from 20% worse hp-fire accuracy, the fire rate elevated to 705 RPM and the magazine capacity was increased by twenty percent. Some may say the Whirlwind is the be-all, end-all, but the S-12 also had a slew of variants to play around with. The Quiet Time brings an integral suppressor to the table while boosting fire rate, talk about interesting! The Tiger Blood, like I already mentioned, boosts the fire rate to the highest of all S-12s, and it is damn hilarious to use. The Vengeance helps with managing the recoil and is the only S-12 variant that comes close to trying to make your shots more lethal. No pellets are added into the shot, but your hip-fire spread is tightened up by ten percent, unique for S-12 variants. The Galant gives two extra starting magazines if you don't want to use Scavenger and don't really want any other buff to the S-12. Unfortunately, the Adroit is the only variant that tinkers with mobility (for the worse, may I add) and gives a sprintout buff alongside a fire rate increase, at the expense of one less pellet per shot. The S-12 is the least reliant on lethality for the shotgun category, so I say try it out and see what you think. It is a marksman variant.
If you like Gung Ho, this shotgun has the smallest hip-fire penalty from the perk, but I still don't like to use it, and I don't want to further increase hip-fire spread.