Well...
Vindicator has biggest crit damage from non-combat shotguns, and drastic damage spread/range - minimal is the lowest, maximal is the highest.
Spread angle is high, magazin capacity highest - 7 shells.
Vagabond has lower spread angle, medium crit damage and bonus +5% precision, 6 shells capacity, minimal damage spread - minimal is highest, but mazimal is lowest. Good as your "sniper rifle"-style backup wepon, before you got decent Tyranny, because it lose precision with distance slower.
Rebel has no high capacity magazine, no high crit, no precision bonus, damage range - minimal is in the middle, maximal is higher than Vagabond has, and lower than Vindicator has.
Tyranny - highest shell capacity, lowest crit damage, but 4 shells in burst, damage range - minimal is ok, maximal is lowest among combat shotguns.
Very good for when you don't have Full Auto, tested by blood.
Despot - lowest shell capacity, highest crit damage, penalty to precision -5, biggest spread angle, damage range - minimal is lowest, maximal is highest. For when you do have Full Auto and you need final solution, and you don't mind to reload every turn.
Or maybe that extended magazine is for exactly that shotgun, dunno yet.
Sovereign - medium shell capacity, medium crit damage bonus, damage range - minimal is high, maximal is inbetween Tyranny and Despot.