Progressive overload is a primary driver for neuromuscular adaptation.

Eventually we adapt to training stimuli and thus manipulating overload allows for continued adaptation.

The two primary overload progressions are increasing load lifted or repetitions completed.

What are the effects of increasing load versus increasing repetitions on muscle strength and size?

What did the researchers do?

The researchers performed an impressive prospective, randomized controlled, single-blind (researchers blinded to the assessments) and intra-subject study (i.e., each leg performed a training protocol).
Each participant’s leg was randomly allocated to load progression (LOADprog) or repetitions progression (REPSprog).

Vastus lateralis cross sectional area (CSA) from both legs was assessed using ultrasonography.
Leg extension 1RM was measured for both legs.

Unilateral leg extension exercise performed two to three times per week for 10 weeks.
LOADprog performed 4 sets of 9-12 repetitions maximum and 90 seconds of rest between sets. The load was adjusted set by set when concentric muscle failure occurred in a repetition outside the repetition maximum zone.
REPSprog performed 4 sets with 80% of 1RM (i.e., fixed load throughout the training program) until concentric muscle failure. Load increment occurred whenever the participant was able to perform more repetitions until muscle failure.
Each leg performed the respective program on the same day, controlling and macthing sessions completed by each leg.

There was no difference in muscle size and strength increases between training programs.
Although the initial relative load was 80% 1RM for both programs, specific load progression for each program meant a different load throughout the study.
LOADprog finished with a load corresponding to 88% of the 1RM while the REPSprog finished with a load corresponding to 62% of the 1RM.

Both overload progression protocols can be used by untrained young men and women to increase strength and muscle hypertrophy in the early stages of training.
This is likely applicable to youth athletes, high school athletes, and freshmen entering their college summer blocks of training.
Only the VL was investigated here so its possible that other muscles would have responded differently.

Progressive overload by increasing both load and repetition may be used to improve lower body strength and hypertrophy in untrained individuals.
As athletes become more trained, "newbie" gains will slow at which point I'd suggest heavier loading for strength gains and proximity-to-failure for hypertrophy gains.
When volume load is relatively matched, strength and hypertrophy will likely be similar, especially for untrained populations.