I was assuming a Middle Earth united under Sauron, with all the Elves, Valar, Maiar, and associated froofy magic gone over the sea. Dragons and such would likely still be around, though pretty darned rare. Take that and give it a connection to Westeros. The Ice & Fire types would probably do much better in terms of tactical action and strategic planning, but Sauron could set up fuckhuge amounts of infrastructure and build massive armies if there weren't conservative terrorists constantly destroying his national relics and oppressing his followers.
An additional note: Magic in Westeros is actually remarkably similar to magic in Middle Earth, in the sense that it's usually fairly subtle stuff, rather than "LIGHTNING BOLT! METEOR SWARM! BIGSBY'S VIOLATING TOUCH!". Sauron would have experience with that sort of supernatural trickery, and would possibly have some of his own, but it isn't the sort of thing that can curbstomp things left and right.
A lot would also depend on how much time has passed since the victory of Sauron over the reactionary forces of stagnation; a decade at the least for stabilization. Give him closer to a quarter of a century and his troops would probably be armed with repeating crossbows, high-quality steel blades, and early firearms. The only reason the Orcs were using crappy swords and bloody awful bows was because the racists in Gondor were deliberately blocking their attempts to gain a supply of good material, in order to perpetuate their bigoted hegemony.