I'll give you my honest view. In my family we have dealt with the top tier accounts of Axis , Kotak, ICICI and HDFC. More or less they are the same. ICICI services are slightly better but there offering aren't attractive.
I would suggest you to take a plunge and open an account in one of the banks. They are mostly same. If you are dissatisfied, then just change to another bank. You can also consider IDFC Wealth but they are a newer bank comparatively.
This is important since their service is highly dependent on staff and can vary from branch to branch.
Give them a chance to serve you and if you are dissatisfied then take your business away from them. All the best 👍