When we sold our house recently, I was told the market was so competitive that real estate agents were advising their clients to chose an offer (all other things being equal) from the local lender vs big online lender. The rational was that the local place was more selective with their appraisers, so the chances of a low appraisal coming through and upsetting the contract were slim. Also, scheduling of the appraisal was more likely to get done on time vs possible 3 week delays. With so many offers being made on a house, it didn't make sense to take the gamble with an online lender and having the contract fall through.
That said, we also just refinanced on a house with PenFed--- a bit different than buying a new house though.