“Maintaining a sufficient stimulus to match adaptive capacity is termed progressive overload.” 1

And progressive overload is perhaps the most critical stimulus for facilitating and sustaining positive muscular adaptations.

In other words, if you want to gain size, strength and performance, training stimuli must progress overtime.

Otherwise, we adapt and no further improvement is achieved.

While progressive overload can be applied with many different approaches and periodization models, most common is some form of load manipulation.

For muscular adaptations, should we increase load or increase repetitions?

What did the researchers do?

In a first of its kind study design, researched compared the effects of progressing repetitions versus load on muscular adaptations.

Resistance trained men and women between the ages of 18-35 who lifted 3x per week were assigned to one of two groups:

LOAD group aimed to increase load lifted while maintaining their target rep range.
REP group aimed to increase the number of repetitions performed while maintaining their initial load lifted.

Both groups trained 2x per week for 8 weeks with training sessions consisting of 4 sets of 4 lower body exercises:

Hypertrophy

Both groups had appreciable muscle gain ranging from ~7-13% across their quads, hamstrings and calf musculature with no meaningful difference between groups.
Rectus Femoris hypertrophy modestly favored the REPS group with researchers speculating that greater fatigue accumulated in the vastii musculature leading to more recruitment of the rectus femoris.

Strength

Both groups gained ~20% in their 1RM back squat with no meaningful difference between groups.
Worth noting, testing was done on a smith machine while training was done with a free-weight back squat.

Endurance

Both groups increased their leg extension endurance by ~7%.
When testing against a fixed submaximal load, research tends to show heavy and light load training are equally viable options for increasing muscular endurance.

Countermovement Jump Performance

Neither group improved their CMJ performance.
This is likely because the subjects were not athletes, did not perform jumps in their training, and both groups were instructed to control the weight eccentrically and concentrically thus reducing stretch-shortening cycle involvement.

Increasing the load and the reps are both viable options for hypertrophy, strength, and endurance.
If the goal is to increase strength, I would still encourage a bias towards progressing load as you get the benefit of strength without the negative effects of volume (e.g., soreness, fatigue, etc.).
If the goal is hypertrophy, take sets to near failure.