For PSU, I personally like SBI.
1. "Almost" everything you can do from internet banking may not be like ICICI but SBI provides more features than HDFC.
2. Availability of SBI ATMs is more. In the digital era, from resetting PIN to changing NetBanking password validation, you can do it from an ATM, with no need for a branch visit.
3. Less charges for service SBI BANK provides.
4. It has SBI e-Corner in all major towns.
So if you want a basic banking lifestyle then SBI is more than enough.
For higher lifestyle value or want to utilize bank freebies then you can look for private players.
SBI CONS:
1. Like HDFC you cannot access/do all account tasks (e.g. KYC update), Cash Withdrawl, or Cash Deposit from any SBI branch free.