It totally depends on your city branch. It's a matter of personal perspective. You can approach both the banks or connect with the corporate RM of those banks and can discuss things that you're interested in beforehand.
ICICI would be better option compared to Axis as they have a lot of branches and options for ATMs.. otherwise the other facilities are available with both banks. Both offer credit cards and loans. Flight discounts available with both.
You can approach both the banks or connect with the corporate RM of those banks and can discuss things that you're interested in beforehand.