There are 2 primary differences - some are gas operated ( Beretta, Browning, Remington, etc ) - some are inertia operated ( Benelli, etc ).
The gas operated guns - need more maintenance, shoot dirtier, have a fair amount of exhaust gases that tend to be in your face ...
The inertia guns - have a little more recoil, unless they mechanically deal with it somehow, shoot cleaner, no gas in your face...
Personally, I like the Benelli - my favorite is the Super Sport - carbon fibre stock, comfort tech recoil system in it - and in a 12ga I like the 30" barrel. I use it as my travel gun / and a one gun that does everything pretty well - vs a dedicated Skeet or Trap gun.
On the gas gun side - I would probably look at the Beretta 391.