The Hek is a monster, great range and nice damage, fire rate is low and the mag size isn't very good either.
Strun is the average gun its price suggests. Can be modded into a powerhouse with time, and the rate of fire isn't completely awful by default. You'll still want to put Shotgun Spazz on it, but it can function without it, at least.
The Boar I never used, and isn't available anymore. Not sure if this change occurs with Update 10 or 11, sorry. Opinion seemed to be it had to be modded a specific way to get any benefits, which isn't what I'd want out of a weapon. I want flexibility, at least to some degree.
The Broncos are, from what I've been told, alright if you can tank some damage. They suffer from severe video game shotgun syndrome, and have incredibly low impact unless you are all but touching the target. The dual Broncos have the same issue, with the addition of a longer reload than what was already a fairly long one, but the damage output might be worth it for you.
The Sobek is my current favorite, but it kind of sucks until you hit around level 25 with it, and that's assuming you throw a catalyst on it. The pellets don't do a lot of damage, but it puts out a ton of them, holds a lot of them in each mag (20 by default, if I recall correctly), and with a levelled Shotgun Spazz, fires with the speed of the modern day AA12 shotgun. Those weak pellets multiply fast, and with armor piercing mods and whatever damage mods you prefer, the Sobek works fools. I like to get a piercing mod in there if I can to maximize the potential of each pellet, too.
The Tigris is, from the little I've used of it, dissapointing. The complaint I saw a lot of when it came out was it only holds 2 shells, which seems like a strange complaint considering it's a double barrel shotgun, of course it's going to hold only 2 goddamn shells. The issues I have are more from it not having any of the advantages one would associate with that style of weapon. You aren't putting out a lot of damage quickly in that 2 shot burst, the reload is middle of the road, and it has the range of a Strun. I like that you can hold the fire button to keep the second shot in the chamber, and release it when you want to let that one off, rather than just fire off both every time, but with the weak damage output I was seeing, the Tigris wasn't what I was hoping for when I heard we were getting a double barreled shotgun.
It also looks pretty silly. I like Tenno designs, but the Tigris is...What happened to that gun, DE?