Of the ones he's won: Qin game for sure. The commerce and food situation was the worst I've seen by a long shot. At least with Freddy he had a nice 18-20 city island with phants, gold, and rivers. With the Shaka map he had food for days and being on the caveman continent did mean everyone there was slow to rifles - and once he took it over he had enough land to win any way he wanted. But the Qin hemispheres? Just about no redeeming qualities whatsoever. Runaway Cyrus with twice the land of any other civ. Two cows, a wheat, and 3 seafood were the only food resources. No horses, no copper, no river, brown land, boxed in, had to move starting settler to be even viable, and perhaps the worst part - being semi-iso with a total psycho. There's a reason I gave up on it after 2 shots - possible, yes, but sooo hard, luck-dependent, and not worth the effort. Partly why I retired my former username. And mad props to Lain for beating it.
Of the ones he's lost: a tie between Qin, and Boudica or Toku isolation. Those two maps were brutal; the Toku island was tiny and crappy but unlike the most recent De Gaulle NC you had no mids to fall back on, no good economic traits to leverage, and almost certainty of runaway + lovefest on the large Pangaea that was medium or high sea level (forgot which it was). Similar with Boudica, though the problem there was less the island being bad (granted it's not much better) but the start being utterly devoid of food (dry rice and plains sheep surrounded by brown tiles are just yuck).
Lincoln one was hard but there was only really one runaway and it just required some creative thinking to overcome (granted, really challenging) obstacles which were apparent from very early on (unlike iso or semi-iso where he had no idea what he was dealing with until contact, and no way to influence things until then). Nevertheless, it's a runner-up for sure. It's perhaps my favorite one he's played so far - nail-biting to the end, succeeding against all odds, and proving that a tank war against 20-city modern-armor/gunship deity AIs CAN be won without nukes.
EDIT: I misread question, as "hardest map" and not "most impressive". In that case, not counting losses, for me it's
1. Lincoln (the tank war was just too epic)
2. Qin (worst. start. EVER.)
3. Willem (just casually winning lib and being tech leader almost the entire game with just 4-5 cities, before taking on a 25-city Megashaka)