Regardless of whether or not you go with the "endorsed" bank versus the other bank, I would go with somebody who is highly recommended through your family or friends. The lending industry is going through a lot of changes regarding restrictions and regulations and fluctuation of rates. I would get a Good Faith Estimate from both, compare them side-by-side, and look out for extra fees. I would also make sure that your lender locks your rate at least through the date of closing so that you do not end up having to extend your rate for any reason. I would also make sure that the lender shows accurate prepaid escrows on the Good Faith Estimate; in the past, I have encountered many lenders who escrow the incorrect amounts on the estimate to reflect a lower amount of cash that the buyer has to bring to closing. This amount then changes after the buyer has committed to the lender. There is a specific formula that must be used when escrowing property taxes, so if you see one lender estimate six months versus 11 months of reserves, take a note and point it out. A lot of lender's can also be flexible so if you have a better relationship with one lender versus another, you can ask them to match rates or fees.
You really have to be cautious with whom you end up choosing because if you exceed your financing period and your lender changes the terms of your loan, you have no choice but to follow through. If you walk away, you will most likely lose your earnest money and the seller could go after you for breach. Bottom line is make sure you trust both your realtor and lender and follow your instincts.