Other than pricing (i.e., the interest rate they charge you), there would be no difference under normal circumstance.
Although Larger Bank have more extensive coverage in branch networks and provide more service, but this is nothing to deal with your mortgage as people usually repay by autopay.
The only relevance is (not every people's concern) Large bank have a higher credit rating (ie., chance of insolvency is low). This will affect your asset when the bank become insolvent as you pledge it to bank.