Since I started diving backmount doubles, I have found that I pretty much always choose to use my doubles instead of using a single tank on my back, even when I'm just doing fun dives. Having all that extra gas is reassuring to me. Having the redundancy, in case of a 1st stage regulator failure is also reassuring to me. If I'm out on a dive boat, I just take one twinset, instead of two individual cylinders. I don't have to move my BCD over to another tank during the surface interval, which is nice. On the second dive, I have all the gas of one cylinder plus any extra, leftover gas from the first dive. Assuming I used less than half of my gas during the first dive, of course.
For example: I use doubles that start at 3000 psi. When I get out after the first dive, I still have 2000 psi left. That means, for my second dive, I have 2000 psi left. In a set of doubles, that is like having a single tank with 4000 psi to use. If I did the same dives with individual single tanks, I would finish the first dive with 1000 psi in my tank. But, I wouldn't be able to use any of that gas during my second dive.
I am now starting to learn sidemount. It gives me all the same benefits that I enjoy when using backmount doubles. But, it means I don't have to carry all that weight of a twinset mounted on a steel backplate on my back. I can get in the water with one tank on, or even no tanks, and then put on one (or both) tanks after I get in the water. And at the end of a dive I can take a tank off and hand it up to someone on the boat, or clip it off to an equipment line, so that I am only climbing the ladder back onto the boat with one tank, instead of 2.
Single tank, backmount doubles, sidemount with independent doubles. They all have their pros and cons. I'm looking forward to being at least somewhat proficient with all 3, so I can use whichever one I want for any given dive. As Doby said, it's just another tool in the toolbox.