I have this mod that put in an amulet that gives 10 to AR. I also have an amulet of Arkay that fortifies health by 10. My question is, which one would be best? How much advantage does 10 AR actually give?

Armor Rating helps defend you against pointy, sharp or blunt hitty things. Health helps defend you against the same stuff plus fire, frost, lightning, absorb health, dragon breath, poison. . . you get the idea.

I've never put them side by side so, I can't provide numbers, as far as physical incoming damage goes. But at early levels, I go for fortify health on apparel, instead of fortify armor skill (or armor rating, in your case).

I don't think 10AR will make much of a difference, whereas 10health, may be that sliver which can potentially keep your character from getting killed. And like Acadian pointed out, there are also other types of damage to worry about -that is, till you rack up sufficient resistance against them.

Yeah, that makes sense. My current character is Breton though, so has some magic resistance, and she's wearing a ring that adds another 22% magic resistance as well. Magic hassn't been a problem really, but the reikling boar riders are very nearly lethal with one hit.

Well; 10 AR are 1,2% less damage... with every (physical) hit. So which one is more useful if you get physical hits depends on how hard you get hit and how often. The stronger the hits and the more of them you get in a fight, the more useful the AR becomes. But ya; the difference is really small, and HP actually help against stuff like magic and poison as well. So I'd still go for that option, I guess. Well, actually I'd chose something entirely different, but I mean out of those two. ^^