The greatest difference between Pilates and Yoga is the path each discipline takes to reach the core. Yoga adopts an internal approach. Pilates takes an external approach.
Yoga begins with stillness. In yoga, time is taken at the beginning of class to find harmony between the body, the mind and the spirit. It is a process of breathing, letting go and becoming present. Once accomplished, the poses and movements become the means for moving energy through the body so your entire system feels at ease, connected and balanced by the end of class. The path towards harmony is manifested from the inside, then slowly, expansively moves outward.
A major difference between the practices is their longevity: Yoga has been around for 5000 years, and Pilates was invented only 100 years ago. To learn more about the origins of both practices, read Sherri Betz’s exploration.
In the end, you don't have to choose between the two. Your Pilates workout can compliment your Yoga workout and vice versa. Do both, mix it up, or focus on Pilates. The key is to keep moving!