IMO, Sidearms, submachine guns and shotguns are awful in PvE.
Sidearms are just a weaker shittier version of the regular auto/burst/scout rifles. The only advantage is a fast switch speed, but that's only really useful in PvP.
SMGs are a shit version of an autorifle with insanely bad recoil. I don't even know what the point of them is. They need to do a lot more damage to make up for the lack of precision bonus damage (not to mention completely missed shots).
Shotguns are just a shit sword.
Are drops based on your current equipment or your total loadout? I know engrams use your best theoretical loadout (even including the vault and alts) but I'm not sure about chests and mob-drops.
I'd like to leave my SMGs in the backpack if possible.
I wish I'd kept my damaged city armour so I could do a quick test.
You should jump on PC and see how shit the hand guns are! Oh wait, your dead before you even saw the hunter with the hand cannon.
Console PVP vs PC PVP, completely different world. People who are good with the hand cannons are devastating.