There are instances when a single-ply system is definitely preferable to an asphalt shingle system (e.g. a low-slope, commercial roof) and instances when the inverse is true (e.g. a steep-slope, residential roof). There are also instances when the choice isn’t so clear, however.
For example, a property management customer of ours recently needed a roof replacement on an apartment building that they manage. The state of the roof was such that the system was considered beyond repair- the owner was intent on a replacement.
The slopes of most of the roof planes were just at the borderline of what is sufficiently steep for an asphalt shingle system (as shingles are water-shedding, not water-proof, an adequately-steep slope is required, per the International Residential Code {R905.2.2}). Had no other limiting variables existed, a single-ply system (whether epdm, tpo, or pvc) would have been ideal.
However, this project was to take place toward the end of January; consequently, the temperatures would have been prohibitively cold, vis-a-vis the bonding adhesive needed for a single-ply system (the owner was opposed to mechanically-fastened and induction-welded systems). The owner also preferred the aesthetics of a shingle system. Finally, as there are trees in the area, the superior puncture resistance of the shingles was a worthwhile consideration.
So, ultimately, after accounting for all variable, an asphalt shingle system made the most sense. Of course, an ice-and-water barrier was installed over the entire roof deck. Additionally, stainless steel nails were used in order to eliminate the possibility of leaks resulting from rusted nails, which, otherwise, would definitely have been an issue, considering the relatively low slope of the roof. Finally, as the low temperatures would have precluded the shingles’ seal strips from activating for quite a while, we applied dabs of sealant over every nail/under every shingle.