The difference will be minor but the benefit is that progress may be able to be continued. An example for me would be on deadlifts. I do 1 set of 5 reps normally (1x5). When progress stalls I'll start doing heavy triples maybe 3x3, then doubles maybe 5x2 then sets of heavy singles or something with speed pulls or a small back off set for volume.
Also there are two types of hypertrophy not just one: sarcoplasmic and myofibrillar. Sarcoplasmic hypertrophy is the increase in size of muscle cells giving you more of the bodybuilder look and mass. This is done with higher reps mainly,think 8-12, but even low rep/heavy weights will have some sarcoplasmic hypertrophy. Myofibrillar hypertrophy involves an increase of contractile proteins in the muscle fiber. This is more strength related and neuromuscularly related than size. Low reps 1-5 are best for this but these reps will also have some carryover to sarcoplasmic hypertrophy as well.