Our understanding of bank pricing is that it starts with  BIS Review 28/2003  5  economic capital and the explicit recognition of the riskiness of the credit and is then adjusted on the basis of market conditions and local competition from bank and nonbank sources. In some markets, some banks will be relatively passive price takers.
In either case, regulatory capital is mostly irrelevant in the pricing decision, and therefore unlikely to cause competitive disparities. Moreover, most banks, and especially the smaller ones, hold capital far in excess of regulatory minimums for various reasons.