If it's on board a S.H.I.E.L.D. Heli-Carrier, then I'm giving my vote to Cap. As long as it's below decks, the combined spaces, which will be familiar to Steve, but not Hal, should be a great advantage. Cap's shield is impervious to anything. So no green beam is getting through that thing. Cap's a master strategist with like, 70 years fighting experience. Hal is a rank amateur by comparison. I take it this is a manned Heli-Carrier, Clint? No way is GL cutting loose with his power ring full force.
Hal can make ANYTHING with his ring. He has a number of ways to relieve Cap of his shield. Make a giant magnet. Capture it into a force-field. Or simply make some giant green hands to grab it out of Cap's hands.
And Hal is a rank amateur strategist? Please! He's led the entire GL Corps more than once, and is in the lead of the group once again currently. Not to mention the many, many single-battles the guys been in against cosmic-level baddies.
The power-level difference here is just mind-boggling. I don't even see how Captain America can even hurt Hal. He's behind a freaking force-field. Cap's fists, his shield, nor a gun or going to do him any good here. Yet on the other hand, one good blast from Hal's ring is all it'll take to put Cap down. Cap doesn't have invulnerability or anything more than peak human endurance, which Hal's ring is more than powerful enough to take care of.
I will give you the home-field advantage you mentioned here. That's the one thing Cap does have over Hal here. But again, the force-field comes into play. At some point, Cap is going to have to come out and fight him face-to-face because stealth attacks from Cap (fists, shield, gun) aren't going to do much more than annoy Hal. Even then, all Hal has to do is scan the Helicarrier and he has full schematics. He can also see through walls with his ring which is something GLs have made use of often in the past.
IMO, this is a walk in the park for Hal. He's in an entirely different power-league than Cap and is far from inexperienced or naïve in battle.