Link is awesome, but Ammy quite literally freezes time to attack with the Celestial Brush.
She fights ferociously at close quarters, tooth and claw and weapon. She can also fight at long range using her Prayer Beads and several Brush attacks. And if he tried using arrows or the hookshot, Ammy can knock those out of the air using the Brush too.
I like Link, but unless he pulls something incredible out of his sockhat, Ammy would win in a one-on-one fight.
In more situations than less, Ammy is likely to take the fight. But considering its a Link with "all his weapons" I doubt the win would be a curbstomp for either one. Nayru's Love or the Magic Armor will keep Link from getting any kind of mortal wounds for a while, and I wouldn't count on the wind spell taking too much effect thanks to Link's iron boots. Given the circumstance, Link would be able to land a few good hits, whether or not Ammy had the Celestial Brush. Win? Not quite as likely, but in this situation, not ENTIRELY impossible, at least not quite.
But hey, at least Link's still got the cooler-looking wolf form (that the citizens are actually scared of).
Link with access to the Fierce Deity Mask could most likely take Ammy. Power of a god in a mask, against the power of a goddess in a wolf statue.
OoT Link would not be able to beat Ammy.
MM Link probably could, with Chateau Romani and the Fierce Deity.
WW Link would not be able to beat Ammy.
TP Link, I really think it depends. With wolf form, and Midna helping, I think he could take Ammy.
Against the Fierce Deity, or a fully-powered TP Link, it would be a very interesting battle indeed.