Different problems, different tools

Pilates was developed as rehabilitation and conditioning. Its logic is mechanical: control a joint through a range, load it progressively, integrate it with the rest of the body. Repetitions are low, precision is high, and equipment exists to grade the difficulty.

Yoga is a much older tradition in which physical postures are one component. The asana practice trains mobility, isometric strength and breath control, usually with no equipment and with progression through depth of posture rather than added load.

What each is better at

Pilates is better at core stability, post-injury rehabilitation, correcting movement asymmetries and progressive loading. The reformer in particular lets you scale a movement precisely, which is why clinicians use it.

Yoga is better at end-range mobility, sustained isometric strength, balance in complex positions, and the breath and attention training that many people come for.

Pilates and yoga compared
PilatesYoga
Primary aimControlled strength and stabilityMobility, balance, breath
ProgressionAdded resistanceDeeper or harder postures
EquipmentReformer, tower, chair (optional)Mat, props
RepetitionsLow, preciseHeld positions, flows
Rehab useVery common clinicallyLess common clinically

Doing both

They combine unusually well because their weaknesses are opposite. Pilates rarely takes joints to end range; yoga rarely loads them progressively. Two sessions of each per week is a genuinely well-rounded program for most people.