As someone holding both ICICI and HDFC cards for a long time, let me draw some comparisons
1. A lot of ICICIs Credit Card busniess operates online, they don't have dedicated people for this, unlike HDFC where every major branch has a card guy
2. Employees that are present at ICICI branches are quite clueless about cards and almost always tell me to refer to imobile app
3. HDFC still has a pen and paper system, like New Application, Upgrade and Limit Enhancement
On the other hand in ICICI it's automated on App and at max you can email them
4. Employees at HDFC branches hold a lot of power and can help you out in getting new cards and Upgrades to Big 3 (Reg Gold, DCB, Infinia), limit enhancement based on your relationship and amount of business you give them
Employees at ICICI either don't know or don't care much as if credit cards isn't really that important to them(I've heard of a few people getting Emeralde Private Metal through brach head by some on TFC, but its quite rare)
5. ICICI gives a lot of importance to Corporate Tie ups and their salary accounts, Corporate RMs can get you a lot
HDFC on the other gives more importance to Alumni of top institute and that's the easiet way to get their Big 3 cards LTF(apart for Ulip route of course)