Local vs nationwide lenders

[Benjamin Papet]

Hi BP community !

I will be buying a primary home in the next few months and contacted two lenders: the first one is my bank (Bank of America) which offers a 3.6% rate on a conventional 30 year-fixed mortgage. The second one is a local lender which offers a 4% rate on the same terms. 

I hear local lenders are more customer service-oriented and all around better, however, is it worth paying more and consequently spending way more over the course of the loan or should I go with the cheapest rate?

Thanks for any feedback you may have !