Ned fought evenly against prime Jaime, and held his own against Arthur Dayne for a short amount of time. TBH the people he's fought are some of the known best sword fighters in the entire series (changed from the book, where Ned wouldn't stand a snowballs chance against Jaime).
Problem is Jaime doesn't have much in the way of on screen feats. Yes his backstory is the same and he was still trained by some of the greatest swordmen in the realm, but it's not a viable feat according the board rules. Going by whats seen on screen in the show, Sandor should win (even though Prime Jaime would slaughter Sandor).
Can't speak much on Dayne since we don't know his mindset as of yet but Jaime was not trying to kill Ned. He also looked like he was enjoying the fight rather than having to work for it. I doubt Ned would last more than a few seconds against a Kingslayer that were trying to kill him
Jaime smiled after their first exchange because he enjoys the sport of it. He probably even went into it wanting to take Ned alive. Rewatching the scene though, Jaime was definitely going all out on Ned. He was even on the defensive for the latter half of it when Ned was gaining ground on him. Their fight was even, and Jaime was definitely trying his hardest. You could see it from the expressions on his face. Plus if he was playing, he would have been able to at least knick Ned here and there, but he couldn't land a single slice.
Jaime was pretty clear about wanted to take Ned alive which immediately handicapped him seeing as how he would have to actively try not to land any blows that could potentially kill while Ned was under no obligation to do the same. Now admittedly we can't really know if Ned was going for the kill either but I'm going to assume he was for now seeing as he buddy was just killed in front of his face as well as all his men
I see why you say you say Jaime was going all out. I disagree but that's more of my interpretation than anything else. To me Jaime was enjoying himself but he did work here just like Mayweather vs McGregor was competitive but McGregor was clearly outmatched.
Maybe I underestimated Ned when I first commented. He would make Jaime work for it but Jaime would win 10/10
If we go by the books Sandor is one of the few people who Jaime thinks are physically stronger than himself and can potentially beat him in a fight. Considering Jaime's high opinion of himself and how many times the two have met on tournaments, that's high praise. Also, in the show Jaime says that after Ned's death there are three people who can rival him as a swordsman - the Clegane brothers and Selmy.
I agree he was clear about it at first, but that didn't mean he'd have the choice if ned is as good as he is. Jaime seemed to actually want to measure himself against Ned in a legitimate fight. He was even angry at the guard member for stabbing Ned in the back before they had a clear victor.
That said, it doesn't really matter here. I still agree the Hound takes it at this point. Prime Jaime doesn't have the on screen feats for me to properly argue otherwise.
No, book Jaime claims there are three people in the entire kingdom who could potentially beat him. The Cleganes aren't among them. He told Brienne that the brothers are stronger than him, but he could still cut through either of the Clegane brothers without too much trouble.
"She is stronger than I am.
The realization chilled him. Robert had been stronger than him, to be sure. The White Bull Gerold Hightower as well, in his heyday, and Ser Arthur Dayne. Amongst the living, Greatjon Umber was stronger, Strongboar of Crakehall most likely, both Cleganes for a certainty. The Mountainís strength was like nothing human. It did not matter. With speed and skill, Jaime could beat them all."
Who the living three are is up to interpretation. Selmy is one for sure, most agree. Some speculated others are Garlan Tyrell, Viper, Areo Hotah, and Darkstar.