I have experience of all 3, though Axis is only couple of months, so need to see how it actually pans out.
1. Axis Burgundy - After some initial frequency mismatch, the RM has been very helpful. He comes home or sends forms, etc by Dunzo. Didn't need to go to the branch. However, LTF CC is only for the main account (others can be add on) and one locker at discounted rate 60%, others only 10%. Accounts can be in different branches. Demat balance also considered for TRV.
2. ICICI Wealth - Has separate Wealth branches, where you get good and fast service. However, RMs in my case have been useless and no help in getting an high variant DC or CC as LTF. No charges. Benefits provided to family accounts. Accounts is different branches. 50% demat balance considered for TRV.
3. HDFC Imperia - pretty bad. only available if all Accounts in same branch. only virtual RM in different city and even after multiple attempts could not get it changed. Demat not considered for TRV. Have to send reminders to RM to reverse charges that should not be charged for Imperia account. Overall not happy