we all know batmans feats but in my gut I feel that Star-Lord will win most of the time because of the following
both are in character, meaning bats will not kill. star-lord however is a little more open to it If need be.
any batarangs thrown can instantly be countered with a hurricane (element gun). if batarangs are some how immune to this, please tell me.
batman will of course be able to win any melee fight, but star-lord is smart enough to realise this pretty quick. quill is no bruce wayne in the brains department, but he isn't a fool.
batman may have a suit for any occasion, but does he carry anti-wind, anti-fire, anti-lightning and anti-avalanche as standard when zipping around gothams rooftops at night? fire and electricity probably. but then his suit will prob allow him full or near enough full protection from fire. but what are the limits to lightning? a lightning bolt hits harder than a hand buzzer. his suit may offer some protection from the cold. but does he ware his anti-mr freeze suit as standard? I doubt it. i'm not sure how it works but star-lord can drop an avalanche if the mood takes him. and that isn't standard gear for bats.
as previously noted, standard stealth tactics won't be at useful as usual. bats likes to go high or in shadow a lot. and star-lords boosters and visor can counter both.
I know batman can fire off multiple rangs and play off angles, but star-lord only needs one hurricane to dispatch them and his jet boots will allow him to outfly them. I acknowledge that on occasion they will hit.
we all know given prep time batman beat any and all (probably the same time) but from what I understand, he standard gear his designed to catch multiple thugs and hoods in the street. with a few pieces of higher level gear for odd rogue. I think star-lords standard gear can deal with gothams base criminal element and batmans rogues pretty well. and Star-lords standard gear is used when fighting the likes of thanos and the badoon.