Consider the bank's/HFC's rate history
The banking regulator, RBI had appointed a working group to study the responsiveness of bank's prime lending rates (PLR) to repo rates. Repo is the rate at which banks borrow from RBI. Ideally there should be a positive correlation between the repo rate and the PLR, that is, with the reduction in repo rate there should be a reduction in PLR to pass on the benefits to customers. The research revealed that government-owned banks were more pro-active in slashing rates as compared to private banks. A borrower can have a fairly good idea by looking at the historic PLR data.
In the period February 2006-May 2009, HDFC had altered its PLR 13 times, out of which it had reduced it four times. In the same period, SBI and ICICI changed their PLR 11 times. SBI lowered the PLR three times while ICICI lowered it two times. However, some of the recent festive offers offer discounted rates without making any amendment to the PLR.
Besides this, take costs such as processing fee, legal charges and prepayment penalty into account before making a decision.
Do not fix on your home lender without finalizing the property. It is very difficult to avail a loan from state-run banks if you choose a resale property 15-25 year old and has had 2-3 owners. The banks also restrain from lending for under construction properties if they are not listed with any of the banks for pre-approved loans.