Do guns of different classes with the same power do the same damage?

When picking weapons, I find it hard to tell which is actually going to do the max damage given that a sidearm, hand cannon, shotgun and sniper rifle can all have a power level of 100 with the same amount of impact. I would hope that a shotgun would do more damage than a sidearm, but I haven't found a way to confirm that short of shooting people and counting the damage numbers that come off.