Here are a few generic points that may help you:
Intermediary vs Direct
1. Even if you have been talking directly to the banks, also try through some intermediary / brokers (like Andromeda, etc.). They are empaneled with multiple banks and generally have an idea which one is under more pressure due to targets & therefore is willing to give a better deal at that point.
2. Some / most brokers will even share some part of their commissions with you, may cover your stamp duty, etc. They'll even do all the running around multiple banks for you.
3. Having said that, if you have enough time & relationship directly with the bank, you'll always get a lower rate than what you can get through a broker. The bank staff can go the extra mile to try and get approvals from higher ups to get you what you want.
% Value
In general all banks will have these conditions - 75% of total cost including stamp duty, registration, etc. or 85% of agreement value only. Please confirm with the banks before looking at only the % numbers.
Interest Rate
The market is quite competitive and the lowest rate that banks are able to offer is mostly the same. I think it is 8.35% now for a normal home loan. Most banks will quote higher than this.
All banks will negotiate the rates. However, before logging in your case, do note - every bank will have to do a credit score check and every hit to check your score reduces your score by 2-4 points. Therefore, try to negotiate as much as possible first, if you think you're getting an offer that you can accept, only then allow them to do a credit score hit. Alternatively, you can download the current date score & give to them along with your documentation.
Normal vs OD/Homesaver/Maxgain etc.
Typically the rate on the OD one is higher than normal home loan rate by 25-50 bps i.e. 0.25 - 0.5%. However, if you are going directly, there are chances that the bank staff can try and reduce this difference making it worthwhile for you to go directly. If you think you'll have a lot of surplus liquidity for short periods of time (few days), maybe going for the OD option is better.
Do note that in OD option, some/most banks have a condition that you cannot pre-pay your loan in part. So the OD loan will continue for entire tenure or you have to fully pay off. Unlike normal loan, you may not be allowed to partly pay down.
Interest Calculation
This is where most banks differ & some are better than others. For normal home loans, all banks allow pre-payment facility where you can pre-pay part of your loan. However, the day on which they consider the credit for calculating interest may differ. Some may also have a condition that you can only pre-pay full EMI / half EMI to reduce principal component.
Do check this carefully. Best way is to ask the banks how they're better than others & they'll be able to tell you everything about what competition is doing.
Hope this helps.