What is the difference between a level I and level II trauma center?

Volume. Mainly volume of patients seen, acuity (how sick the patients are) and amount of research done by the centers. Level 1 centers tend to be busier, see and handle sicker patients and do research. The more severe your injury, the higher level of trauma center you want to go to. Level 1 is the highest.
More expertise. A level1 center is a teaching hospital or institution. It may provide more expertisein in things like heart surgery after trauma and and certain neurological injuries.
Research Training. The level i and level ii trauma centers provide comprehensive trauma care. Both centers have 24 hour coverage of surgeons, anesthesiologists and speciality services. Level i trauma centers increase survival of critical patients by 20+%. The level i center also has extra speciality coverage, as well as research and training programs to provide expertise in trauma care.