He is definitely more Asgardian than Frost Giant after Odin's magic and the process was basically permanent. The only time he progresses back to frost giant looks is when close to frost giant magic or touched by them. If he was still a actual frost giant he would have been broken in pieces from beating like Thor, Hulk and being hit with the destroyer weapon.
To me it seemed that scene in Thor was meant to tell us that Loki's a Frost Giant (an enemy of the Asgardians) and that his Asgardian appearance was just a skin-deep façade.
If it was only skin deep though, why would he bleed when trashed and not be broken into bits when smashed like the rest of the giants. I'm thinking it was a full transformation cept when he is exposed to dark magic.
To be fair, what Frost Giant qualities has shown anyway? He turned blue and that was about it. He didn't grow in size. His face and shape didn't change to match those of Frost Giants. He didn't show any skill towards ice or cold manipulation.
I'd say it's his Frost Giant heritage that's only skin deep (thus only changing in skin color). Everything else about him is Asgardian.
Anyway back on topic, I don't see Cap putting any lasting hurt on Sif. Sif for the win.
I think the point that needs to be made is that Loki was never considered tougehr than any of the other Asagrdians he was with.
IF his fight with Cap is any indication which it very well should be. Cap just is not capable of physically matching any Asgardians comparable to Loki. In fact it seems heavily implied that in terms of fighting prowess Loki was the least capable person out their group.
So Sif should have at least as easy a time as Loki did if not a better chance.
Loki was toying with him when they fought, and let himself get captured to further his plans. If he, or any of the actual skilled Asgardians, got serious with Steve, Cap would get his ass kicked.
__________________ Never take life seriously. Nobody gets out alive anyway.