Hi Erin! A very good question. When I’m training a client for flexibility, I generally pay more attention to “duration” rather than to “number of repetitions or sets.” In my opinion the key to gaining or improving flexibility is duration. With my answer, I’m assuming we’re talking about static stretching, and so, generally with static stretching you want to encourage holding the stretch for a period of time rather than concentrating on how many time the stretch is performed. Of course, in a “perfect world,” holding the static stretch for a period of time AND performing those stretches for more than one set of stretches is perhaps even better, but since your question asks an “either/or” scenario, that’s what I will respond to.
Given the choice between one set with holding each stretch for a significant amount of time (meaning one that effectively challenges and improves flexibility) versus what I unfortunately all too often witness in some gyms of quickly moving through each stretch to “get finished” (holding the stretch for 5-10 seconds if they’re lucky) and perhaps doing multiple sets of that “short duration” stretching, I’d take the ONE set performed properly.
I hope this helps, and answers your question.