This is my first post on a battle on this site and I have found it to be one of the most difficult, being both a star lord and batman fan. (Blaming both the comics and movies here) But I'd have to give it to Star Lord, (Batgod preserve lol) Wayne has the advantage here in H2H, advantage taking Star Lord almost 7/10- 8/10 in this but I think the big advantage here would be the tech and maneuverability and even Star Lords unique "unorthodox genius lack of discipline." Quills tech, even with standard gear, is something I think batman would never see coming from a mile away. His element gun, boot jets and any other little trick he has stored in his bag can return whatever Batman has I'd be interested to see the tactics employed by both, since they're thoughts on killing seem to be the polar opposite. If Bat's gets close here, its a wrap for Quill even with his skill, the tech here would be the thing to watch, I feel like Peter would just have a leg up just because hes so much more used to fighting on a grander scale than bats.
Peter wins here in one of the toughest fights of his life. 6/10
If Peter knew Batman is just some dude in a batsuit, Quill would way underestimate bats ability and lose. As soon as Peter goes H2H, this fight is over. That said, Peter is used to cosmic-level threats and opponents--and while he may never have a plan, he still isn't going to start by trying to punch batman in the face. Starlord is far more likely to keep this fight a long range battle, and his alien tech should be enough to keep batman down.
Basically, I think this battle comes down to Batman's primarily street level threat experience vs. Peter's galactic level threat experience. While Batman has the much better strategy, H2H, etc. he just is not going to be able to keep up with the element gun--especially since Peter is going to be much less worried about collateral damage.