Axis is one of the good bank to have an account with, as compared to HDFC, ICICI, KOTAK. It is the chepest bank in terms of the charges, processing fees or any service fee like locker or dmat account. AXIS will not give you very high end service but also will not disapoint you. it manage to be modrate. PRIORITY account is the service where you dont have to visit bank, but bank will visit you at your doorstep.
You can demand every service at your home in priority banking. Just dont invest in there life insurance policies or any other investment plan. they are not good.