Negotiate Salary to Subcontractor Company

I've been interviewing for a 'Dev Shop' that does software development work for Big Bank Corp. So there's some sort of relationship where Big Bank Corp. has their own in-house engineers, who also work alongside 'Dev Shop' engineers placed in their office.

I've interviewed with both companies, have been approved and have received an offer.

I'm familiar with Patio11's essays on salary negotiation, however I'm not sure about the dynamics of who pays who how much between these companies, and how much room I actually have to move upwards.

I'm continuing to interview with another company. Does anyone have insight on contractor payments/relationships? How is 'Dev Shop' compensated for my work?