For me, it mostly depends on the size of river. For anywhere that requires consistent casts of, say, 60' or so I would choose a double hander. Although I can cast these distances with a single hander, I find it much less effort with the larger rod, which avoids the need to strip line, and a longer rod also has big advantages in terms of line control.
But much of my fishing these days is on small spate rivers rather than the 'classic' medium & large rivers. On these little rivers pools more than 30' wide are uncommon, and many are no more than 15' across, so most of the time there is no need to cast more than about 30-40'. Clearly for situations like this a double handed rod is overkill, and can actually be a disadvantage. I still prefer a longer single handed rod though (typically 10' 7wt) for the line control it gives. You rarely need anything more than a floating or possibly intermediate line, and smallish flies, so that's not a reason to need a big rod either. These rivers also tend to hold small fish, predominantly grilse, and they give a better account of themselves on a light rod.
I can't say I have a preference between single and double-handers - I love them both for different reasons. Big water 'combative' fishing, possibly involving deep wading, and banging out long casts with a big rod has its attractions (and these rivers are probably more productive), but I love the subtlety of a day on a small stream, travelling light, probably walking several miles, and fishing 'pocket' water with what amounts to little more than heavy trout tackle. But to me they are almost like different disciplines, and funnily enough I can't think of many places I've fished where I've faced a real dilemma over which rod to choose; generally the river and the conditions seem to make the decision for me.
It's perhaps worth mentioning a couple of 'minor tactics' which break the general rules. 'Backing up' is one such, which requires quite a bit of line to be retrieved during the swing - I find it easier to false cast and shoot this line with a single-hander (I suppose a short-head spey line on a d/h rod might do the job - I don't own one though). 'Dibbling' is another technique that can be effective in low water conditions. It works best with not much more than one rod length of line outside the tip ring, and a long rod may be useful, even on medium-small waters in low-water conditions. to gain extra water coverage. But these are not classic, mainstream methods.