Vinyasa, which means breathing and moving, uses the same principles and foundations as Ashtanga but the sequence is different each time (by the teacher's design), allowing the student to work on being present and calm no matter what comes their way during class. Creating stillness of mind even while the body might be shaking or falling over.
Both Vinyasa and Ashtanga offer an excellent balance of strength and flexibility. Both strengthen your heart and increase oxygen intake, improving your health and vitality. And with both, you will learn to discipline your mind as well as your body.