hmm
I dont think I would have taken Ned over the other challengers in this round but I'll break my reasoning down a bit here why I think he could become victorious over Mr. Drogo.
First what has been talked about the most in the thread is the fighting style and equipment differences. If both men are on the ground in a duel or trial by combat situation I think it goes to Ned's favor in this regard. Ned has better armor, and paticularily considering that Khal is using a curved blade. Mail and plate are strong against slashing attacks but not great against piercing, and a curved blade seems to be more of a slashing weapon. (Again along with bow ideal for mounted warfare). Ice would have no problem getting through a leather vest with copper disks. However the case for Khal in this circumstance, would be if he took the tactic that Bronn used in Tyrion's first trial by combat, dance about and tire the more heavily armored fighter.
If both men were ahorse, I'd undoubtedly need to go with Khal, for I think ahorse Khal would be a match for any rider in Westeros (imagine a full feild and Khal on one end and a Jaime or Loras on the other).
Secondly, historical prowess. Khal's braid states he has never lost, and he commands the largest Khalasar (sp?). Ned Survived the War with the Targaryen, The Tower of Joy and the Uprising of the Iron Isles so he never "lost" so to speak. Ned was also the Lord of the largest (albeit least populated) of the 7 kingdoms. His kingdom had the usual riffraff plus wildings, deserting crows and folk like Shagga. So to me in this regard, they are very similar, neither one quite gets the favor.
Clearly Ned dies after breaking his leg and being taken into custody and the unfortunate removal of his head. Khal would have none of this, Khal I do not believe would serve another King. (This is the Cultural side, as opposed to the afformentioned Technology side between the two men). However, Khal did die of injuries sustained on a raid of the Lamb men (shepards? not the most impressive death in the series IMHO.) I have to give the edge here to Khal. (Shepards!!)
Unfortunately both men had to be dispatched in the first book, so other than reputation we get to see neither of them really fight, unlike many of the other participants in Wiggum's tourney. Obviously Ned lives, No war in Westeros, Khal, likewise, no dragons.
But in the end I had to take Valyrian Steel, Chain and Discipline over an Arakh , Strength and Savagery. I believe the warring strategies of Westeros favor one to one combat over the raid and pillage tactics of Dothraki.
Edit: Assuming Ned and Jaime win this round (which looks likely) This may be Ned's last hurrah. Next round he draws one of the following:Victarion, Arthur Dayne, Sandor, Bronn, Syrio, Barristan or Jaime. He seems greatly out of place in that group.