Over the last seven or eight months, I've been rotating single bell C&P programs with double bell programs: various permutations of DFW, Giant 1.0, the 5TRM program from an article on this site, and now a program of double clean, press and FSQ complexes that I designed and am giving an experimental run. During that time, I have run both Giant 1.0 and the 5TRM program as both doubles and singles. I haven't strictly alternated singles and doubles, and have probably done more doubles in that time.
I think there are advantages to mixing it up.
The technique is different so it's a nice mental and neurological challenge to focus on refining two different grooves. I suspect there's some same-but-different, specialized variety synergism between them, both in terms of carryover from one to the other, and also in giving your body a break from the same thing all the time.
I can lift more weight, or the same weight for more reps, with singles, so rotating between them gives some additional variety in loading and volume. I definitely feel like there's a role for using single-bells to transition to heavier weights for doubles.
Besides the difference in technique, there are two other big practical differences.
One is that with doubles, you get in lots of double cleans. So your cleans are twice the load and there's a significant effect on hinge power and conditioning from the cleans. With singles, the cleans are much lower powered, so even though you do twice as many, the power component is way, way submaximal. Even though you're doing twice the hinge reps, it feels subjectively like a lot less work.
Two is that your time under tension for all your core and stabilizer muscles is twice as much. You have to keep getting tight and staying tight twice as many times, for twice the total time. It also means you are starting your second arm reps right at the time you would be done with a set of double bells, so you're starting that second arm set in a fatigued state. That's why I always go first with my non-dominant side, because I want the rest of my body to be fresh when I'm pressing with that arm.
However, when I did an RM test at the end of my last single-bell program, I did it the other way, dominant side first, but I rested 10 minutes between sides (in regular training I always switch on the fly and do both sides without putting the bell down). I did it like this because I wanted my strong side to set the pace and put up the biggest number possible for my weaker side to try to match. I felt like mentally, my weaker side would tend to give out sooner without that number to shoot for. I then took a nice long rest so the rest of my body would be fresh for the presses on my non-dominant side.
I don't know if I would call doing both sides separately as necessarily more "conditioning" in a general sense. But in a specific sense, I did feel it had some carryover to shorter sets with doubles. My body was used to staying tight for longer and more reps in a row, so it was easier to stay tight though shorter sets.
One additional point, which is sort of related, but not directly to singles vs. doubles. In my complex program that I've been doing for about the last month, on the lowest volume day, I have been doing all the cleans before the presses and doing consecutive MPs instead of C&P. The MPs have a very different feel. They are more locally fatiguing to the pressing muscles because you don't get any break between press reps, and the skill of getting tight in the rack is different when lowering from overhead compared to catching a clean. I've done a lot of straight MPs in the past, but not for a long time, and since I started this recent emphasis on C&P programs I have only done C&P, so it's been a bit of an adjustment. The rhythm of the C&P feels really good to me, so that's still my focus, but I'm seeing a lot of benefit to mixing in straight MPs.