Attached are two articles which is related to your requirement

Dear Marcin, good question! Usually we expect that large firms have better perform than small-medium ones. 

Below you find a paper, in urban transportation field, which shows the opposite side.  Small and medium operators operate more efficiently in large urban centres than large firms because they have more knowledge of the traffic and local. Although this paper does not investigates whether those firms create a competitive advantage for supply chain members, I believe it will depend of the type of chain, sector and where it will take place. When we consider a large territory, for instance, it makes difference. In this sense, it is also important to differentiate the role of LSP of Carriers.

http://www.sciencedirect.com/science/article/pii/S0967070X15300263

Another paper below you can find different viewpoints of sustainability initiatives of freight operators. Although, again, there is not focus on competitive advantage, indirectly these actors may influence their supply chain members. In section 6.1 "Lessons learned"  maybe there is some insights for future research.

http://www.sciencedirect.com/science/article/pii/S0149718915000853

Hope these discussions/concerns can be useful. If you have any question, let me know, please.

Best regards, José