Experientia magistra stultorum.
Accepting that we're talking about Game of Thrones, and not ASOIAF, it may be hinted in the show that raw skill is only one dimension of a great sword fighter. Surrounding the Ned/Jaime showdown, there are a few dialogue exchanges of which I took note:
- Jaime says he looks forward to facing Ned in a tournament, as the competition has become a bit "stale" (S.1 E.1) Ned replies "I don't fight in tournaments because when I fight a man for real, I don't want him to know what I can do."
- Ned insinuates he wouldn't stand a chance against Ser Barristan Selmy, widely considered one of the greatest swordsmen in the Realm (S.1 E.5) Selmy replies "You're too modest. I've seen you cut down a dozen great knights."
- Earlier, Jaime compliments Selmy on his dispatching of Simon Toyne, leader of the Kingswood Brotherhood, while Jaime was still just a squire (S.1 E.3) Recounting their duel, Selmy only says "Good fighter, Toyne. But he lacked stamina."
- When held in the black cells and acknowledging his grim fate to Varys (S.1 E.9) Ned asks "You think my life is some precious thing to me?"
Whereas Jaime was given exceptional training and cultivated among knights such as Selmy and Ser Arthur Dayne, he had yet to experience the rigors of a true conflict, his closest experience coming from an entanglement with the Kingswood Brotherhood while he was still a squire; Selmy and Dayne did most of the real fighting.
Ned, on the other hand, was much more seasoned in combat, having taken the field in both Robert's Rebellion and the Greyjoy Rebellion. Selmy personally saw him "cut down a dozen great knights", and that doesn't include Ser Gerold Hightower at the Tower of Joy (S.6 E.3) as Selmy was not present for that fight; while ultimately bested by Dayne, whom Ned considered the greatest swordsman he'd ever seen, Ned did survive the one-on-one onslaught long enough for help to arrive.
Strictly on personality, you could fairly judge Jaime as cocky, disdainful, and dismissive, whereas Ned is subdued, steadfast, and humble. Jaime acts as though he has something to prove, and Ned does not.
So, finally, breaking down their fight (S.1 E.5).
- Ned makes the first strike and the second, anticipating Jaime's forward thrust well enough to get a fist on his shoulder, shoving Jaime in the path of his momentum. If Ned were carrying a dirk, Jaime would be dead.
- Jaime overpowers Ned with the following strikes, and when they turn, Ned anticipates a feint and nearly slashes Jaime's face. Jaime is impressed. Ned remains focused.
- Ned remains defensive on Jaime's following barrage; when the fighting gets too close, Ned waits for an opening to cut and chop high. Jaime attacks in response, but Ned stands his ground, counterattacking low to back Jaime off until they finally cross swords again.
- Jaime attempts to push off, but Ned doesn't budge. A genuinely confounded look washes over Jaime's face, while Ned remains unphased.
- Ned is the first to disengage, and he is stabbed in the thigh.
Now, what we see is simply a very evenly matched fight. In terms of context, however, Ned has regularly fought stiffer competition in life-or-death situations and does not concern himself with whether he lives or dies. Jaime has fought safely in the company of the Kingsguard or in competitions and believes himself, rightly or wrongly, to be the best swordsman in the Realm. However, he has yet to truly see his life endangered.
I would argue that Ned may be the less skilled swordsman in the truest sense, but what he lacks in skill he makes up for with experience. He's looked death in the face by fighting more skilled swordsmen and surviving, learning to embrace his limitations by focusing on responsible defensive technique, stamina, and picking his spots. In this fight, Jaime confronts the possibility of his own mortality for the first time. In this moment, Jaime's façade melts, and Ned watches it happen.
Now, does that automatically translate to a Stark victory? No. But if Jaime begins to doubt his skill halfway through a fight, Ned has put the odds in his favor. Experience is the teacher of fools.