Hopefully this isn't a stomp. Base Cap and Base Quill, Captain America has an 8-B shield but Star-Lord also has weapons capable of harming Korath, shredding Ego's Avatar, restraining Spider-Man and Iron Man as well as threatening to kill Spider-Man with his Quad Blaster. Cap does have the strength advantage though, as well as a shield which can block High 7-C attacks.
8-C versions, Captain America has the vibranium shield, Star-Lord has all his weapons, in-character, 30 m starting distance, other than that Standard Battle Assumptions
Cap tries to get close while Quill can play keep away, range spam or throw bolos and grav mines to pin Cap. Stun rounds bypass the shield (cuz lightning that spreads over the entire body) once his plasma fails. Voting Quill.
@Kidkinsey Star-Lord is significantly weaker than Captain America, as the former is "at most" 8-C (he got outclassed by Gamora), while the latter is 8-C. So I would say Star-Lord is not capable of incapacitating Cap with his physical blows, however he can do so with his gadgets as they are able to harm far stronger characters than Cap.
if cap is able to get id give if it to him if peter attempts to zone him out cap will throw his shield that id assume can take anything peter can dish out, however im still going star lord due to the 30m starting distance and the reasons people gave above