Eric, I would say that from what I have learned as a sidemount diver is that the main difference, besides having double the gas supply with you and the convenience of that, is that you are self-sufficient with 2 separate life support systems.
Additionally, in tight spots like bedding planes or small passageways, one can either belly out, or push a cylinder in front to themselves, to gain access easily.
Also, there is a lot of range of motion for the diver’s head without having any tanks behind them. As a photographer, this is very nice.
Other perks would be that for those of us who are aging, or have prior injuries that they have sustained over an active, sports related lifestyle, tanks on each side alleviate pressure points on the spinal column.
Unlike walking down to a site with doubles on their back, sidemount cylinders are easy on a diver to carry via a cylinder strap, or by using a dolly.
Plus, say that you finally wanted to explore the inner chambers of the mansion of the cave system that you had been spending all your time at the front door...well, to be properly rigged for your training to enter, would get you there that much faster. :-)