Rajasic Yoga - the most popular emphasis today is pushing too hard, the reason for so many injuries. While working hard has its health benefits and tone there are many injuries due to teachers pushing form regardless of students body and its limitations. Anatomy is given mild attention but no school seems to understand ROM, bodyreading, or kinesiology.
Iyengar Yoga - am certified in Iyengar yoga in 1976, so my training is quite old. Iyengar students become quite weak, tested with more weakness in MT than any other system - up to 12 for some senior teacher. Benefits lots of anatomy, downside sometimes it is unclear. No kinesiology presentations except mine.Also Iyengar's book Yoga has for instance has chart of 21 muscles - 7 of which are wrong. Some depth in Yoga Sutras lacking in other systems.
Kripalu Yoga has lots of inner awareness but no clarity on what asanas are core or how to do them in uniform manner. Some meditation practice though not uniform. There are some elements of classical yoga though it seems to change frequently so hard to find agreement amongst their teachers as to what are characteristics of this practice.
Bikram Yoga - lovely routine and strong for those who are in good health. For those with excessive kapha and need of detox the heat is a good idea. A main downside is hyperextending knee is emphasized. Most common injuries are to knees and tendency for repetitive motion injury (RMI). no subtle body practices.
Asthanga - Flow - Vinyasa Yoga - strong routine done for excellent health. Optimal benefits to ROM and MT. These are among the healthiest surveyed however much incidence of RMI, teacher induced injuries, and verbal pushing into more flexibility.
Viniyoga - Desikachar & Gary Kraftsow - lovely gentle system, adapts practice to mild form for needs on individuals. Like I Yoga they tend to gain modest strength yet are mildly weak though have normal ROM. Gary has depth to his teaching though he rarely gives it - knows the texts and subtler practices but focuses on asana, and vini programs for health and back maintenance. Did a major study on benefits for back care. He wants to tap into the 100 billion dollar market for back pain. more power to him.