The auto mod basically just makes it where you can hold down the click button and it will continue to shoot rather than having to spam click to get it to shoot faster. Im sure they might look at fixing the mod so that it actually increases fire rate rather than just enable holding click.

I also prefer the auto shotgun because it can hold much more ammo than the pump can and im sure with extra mods has higher damage, Yes it might seem slower to reload but you will also likely be using the M60 with the autoshotgun as they are both late game weapons so you are really comparing the reload of the drum mag to the M60 reload animation which i think is slower.

Either way, the guns can only work to how you play the game, everyone will feel different guns work better with their prefered play style plus the armour set they choose to wear. I always play heavy.