In yoga, you are working muscles close to their limit while your joints are at the limit of there range of movement. This is a very efficient way of working out when all goes well, but if something gives way, there is the risk of injury. In Pilates, you are never supporting your own weight while pushing muscles and joints to the limit.
Pilates has a wider variety of exercises you can do and the benefits are far better than those doing yoga. Pilates not only stretches muscles, but also tones and strengthens them as well. It can be made to be fun as you can do exercises to music. Pilates is overall an excellent exercise for women.
Pilates involves more physical working out than yoga does, even though they both only utilize the body and its own weight to work out. Yoga can be very strenuous on the body and uncomfortable while I believe that Pilates is safer for the muscles and structure of the body. Yoga can sometimes lead to dislocation or even muscle tears if not being directed by someone who knows what they are doing.
Simply put, the practice of yoga includes the movements of Pilates. Practice of Pilates, however, does not include the whole range of yoga.
Yoga is a very diverse practice. Pilates is a very well-defined, stagnant pathway.
One is a spiritual practice which leads to a firm healthy body, the other is a physical therapy exercise which leads to very specific type of healthy body.
I don't think one can say for certain that pilates is better than yoga, or vice versa. Both are forms of exercising and working out, and that doesn't mean that one is better than the other. They both have their own respective pros and cons, and are very different in ways.
Pilates is not better than yoga. Pilates is great and offers many health and body (physical) benefits, but yoga also centers the mind in a way that Pilates does not; yoga offers an additional dimension of well being that keeps a person's mind and spirit in shape as well as their body; Pilates does not.