Anyway, now that I have some time, I can't really see Cap solidly winning this one and at best he can pull an inconclusive
That said, I'm leaning on that more then Luffy for the following reasons.
Cap is amazing at dodging, the blog points this out above but in case some people don't wish to skim through
-Dodged every attack from Daredevil, an acrobatic with ehnhanced senses that border on Precog.
-Was able to quickly defeat a dude who was able to download all the knowledge on Martial Arts the internet had to offer again not getting hit once.
The shield only capitalizes his dodging.
Now for some counter points.
1. Luffy throwing the shield won't work, Cap has a Vibrinium gauntlet on his left and right arms that can call it back to him.
2. Luffy may get the shield out of his hands, but then Luffy is stuck with a shield he has barely any knowledge how to use while Cap has over 100 years of expirience with it (No really, check the blog)
3. Caps standard attacks won't do much damage, however, his Shield Throw and shield punch will, due to the Vibranium physiology of the shield, its razor edges will bypass said physiology and Cap can punch with said razor edges. (There's a Far Higher on his profile detailing this)
Now with my main point, Luffy is going to have massive problems hitting Rogers, his lifting strength will be an issue but his standard attacks will either get precoged and dodged or just blocked with the shield, Luffy will also have to keep the shield away from Cap because if he attempts to throw it Steve will call it back and know not to do said strategy again.
Now in regards to holding the shield, the Shield lacks a proper arm guard (For those that don't know that's basically the straps underneath the shield that allows people to hold it). Caps gauntlet replaces the arm guard with his gauntlet, so Luffy has a choice between very awkward s holding the shield without an arm guard, or just throwing it, considering the latter scenario makes much more sense on paper I see Luffy throwing the shield and Cap calling it back.
In summary, and adding what Calaca said.
-Steven has expirience and victories against people far more skilled then Luffy without said people getting a solid hit
-Luffy's stat gap and Blunt force resistance means Cap is forced to Punch with the shield or throw to do proper damage to him, but considering its sheer sharpness and vibrainum it can absolutely do major damage if it hits.
TLDR I think this can go either way and I vote Incon