I am using Axis priority account .. There are no extra charges levied till now .. But there are hardly any offers .. also for personal loan they did not even waived off processing fee which was very bad ..Dont know if its same with hdfc ..Also Axis RM will call you every atleast 2 times a week and he will try to always market some or other schemes related to ulip/sip/ insurance etc and tell that this offer is only for priority which is a big fake..Stay away from all RM they are just good till u buy smtng thru them..
Dont know much about ICICI if there is a similar behaviour