Boots, the coach guns often are plain cylinder bore, without choke options. Longer-barrelled SxS guns will usually have chokes. (Of course, you can have the barrels fitted with screw-in chokes quite easily.)
The EAA Baikal is a good gun, over-engineered to the point that it's almost indestructible. It badly needs the services of a good gunsmith to give an acceptable trigger pull, and the action is usually VERY stiff to open until it's broken in (again, a gunsmith can fix this). It's very popular on the Cowboy Action circuit, and there are plenty of gunsmiths who can do an action and trigger job on it. There are two models: one with internal firing pins, and one with external hammers. The early model with "external hammers" actually had dummy hammers: the firing pins were internal, and the hammers merely served to cock the action. The current model has actual hammers that fire the shells.
The Stoeger is a very good coach gun, albeit less "massively" constructed than the EAA. It, too, could use a gunsmith's attention to action and triggers. I liked mine, and found it lighter and easier to handle than the EAA.
A couple of things on both these models:
1. They have extractors, not ejectors (which are illegal in Cowboy Action shooting). Many competitors have their chambers honed, so that the low-power shells they use will fly out of the chambers after firing by simply "flicking" the open shotgun rearward. However, this won't work with higher-power shells like buckshot or slug.
2. Their sight is usually just a bead, and in these cheaper guns, as often as not, the bead is off-center. I'd recommend looking at this carefully, and perhaps replacing the factory bead with something like the Express Sights "big-dot-style" bead.
3. They usually have two triggers. This is an advantage, IMHO, as it gives you instant choke selection if you install chokes: but it also calls for care in the operation of the gun. If you shoot the gun with your forefinger on the front trigger and your middle finger on the rear trigger, as I learned to do in Africa, you need to develop the habit of shooting with the rear finger first, then the front finger. Do it the other way round, and the back of the front trigger will push against the top of the middle finger on the rear trigger, with predictable results. A double discharge of buckshot or slugs out of a lightweight coach gun does interesting things to your shoulder! Don't ask me how I know this...
My current "coach gun" is a Stevens Model 311 20ga. that I had cut down. You might want to look at the 20ga. models: for HD use, they're almost as effective as the 12ga. models (a 20ga. buckshot shell has the same energy as two .44 Magnums, which is nothing to sneeze at!). The recoil is considerably less.
Slugs can be fired, but accuracy will, of course, suffer in the absence of a set of sights. You can get hits out to 50-60 yards with a bead, given practice.
Finally, most of these coach guns come with no recoil pad at all, or at best a rather ineffective one. I'd strongly recommend trimming the stock to fit you and adding a
Kick-Eez or
Pachmayr Decelerator recoil pad. These help considerably in reducing felt recoil.