a small sg-90 servo draws 100-250 ma. a 9V battery only has a capacity of 400-600 maH, can provide that much current for only 1 hour. a AA battery has a capacity of ~1500maH
using a 5V regulator reduces the voltage but not the power consumption. if 100 ma were being drawn, 400 mW (100 * (9-5)) would be dissipated (wasted) across the regulator