Pilates focuses on physical body strength and a strong core whereas in Yoga we seek inner and outer balance, flexibility in the hip joints, spine, ankles, shoulders, expanded muscles and ligaments around the joints which give the joints space to move. My own experience with pain in the lumbar area taught me that both are important – a strong core and strong back muscles for a supportive healthy spine. Therefore, I have been attending Pilates classes just to train the postural muscles, i.e. my core. My back muscles were already strong from regular Yoga practice. What I do now is, I include specific postures for abdominal strength in my daily Yoga practice and share it with my students in the Yoga class as well.
In Pilates you learn the precise breathing technique while you are doing abdominal work. I assume you know many exercises to work on your abdomen but you may not know the correct breathing technique. However, this is not the only secret to getting strong abdominal muscles. In postures where you have to lift the trunk you should be aware of and have to work on your trunk as well. The chest must be open, groins long, shoulder blades down the back and back ribs pulled in. To improve this motion, Yoga would give you better awareness in that part of your body.
In summary, if you are ‘just’ looking for a strong core you might choose Pilates. Yoga involves abdominal postures as well but is more focused on building strength and balancing it with flexibility. The practice of Yoga aims at overcoming the limitations of the body. Only in Yoga can you keep both the body and the mind relaxed, even as you stretch, extend, rotate, and flex your body. This includes attention to detail in every part of your body and alignment to the skeletal body. This accuracy and attention to detail is not merely a physical effect but involves also physiological and even psychological processes. Everyone has their own needs to keep the body fit and healthy and these will lead you to your decision.