I don't know that any one can say that a 22" barrel will be more accurate than a 20" or even an 18". Every barrel is its own story. I use 2 guns, an Ithaca Deerslayer II with a 24" and Rem 870 with a 22", both scoped. My hunting partner has a Rem 870 with a 20" tube and scope. They all shoot about the same overall, but they all respond differently with different brands of slugs. Expecting a single brand of slug to shoot as well as another is about as reasonable as expecting different brands of rifle or pistol ammo to perform equally. Each of my guns has a particular favorite brand, including my partners gun. We had to shoot a lot of slugs to find out which gun need which slug, but with experimenting, all barrels ended up shooting pretty much the same. My partners 18" will shoot right alongside my 22" barrel. My Ithaca will outshoot both of them.( we are only talking fractions of an inch) I doubt it is the barrel length but more the care in manufacturing or maybe just plain dumb luck.( I like to think it is because Ithaca does a better job with rifled shotguns)
As far as distance, I doubt you will be able to tell the difference between any of the barrel lengths in actuallity. There may be some, but not enough to be concerned about as slug guns aren't really a long range proposition. I know there are those that will argue 50 fps gain to their death bed and a 1/4" difference in accuracy til the cows come home. This is why you sight in at the ranges you expect to be shooting at and some shots at longer distances to SEE what the gun does.
My partners 18" is fast and easy to handle, but it recoils a lot harder than my 24" ( the Ithaca simply weighs more) I never had a problem with a 24" barrel in the field, as I can surely swing the gun a lot faster than any deer can run so I think that long vs short is more in the "mind" of some, but of little real difference in performance or convenience.
It will boil down to the fact that no matter what you hear about any gun or barrel length, the bottom line will be what YOUR gun will do. There is no accurate way to predict accuracy ahead of time only shooting will tell.
I base a lot of my observations on having shot thousands of slugs through many guns with many different brands of slugs including handloads. Buy the one that pleases you most and fits your needs and desires and then go shoot it with a bunch of slugs and see what it will do. Good luck in your choice