My favorite thing* about Jaime and Brienne's duel in ASoS is how BOTH of them come away from the fight absolutely shaken by their opponent.
Especially on Jaime's side it, would be so easy for him to just excuse it as a fluke because of his chains and year of imprisonment. Indeed, that's how Brienne sees it! But nope, he's just floored by the fact that she's stronger than him, and fast and skilled enough he can't run rings around her. Which is what he expected, even with the chains and muscle loss.
(*Yes, ok, Jaime narrating the duel in a weirdly sexy way is a close second. I bet he does that for every (good) sword fight. He's so horny for (literal) swords. Love that for him.)
Jaime while getting his ass kicked by the Maid of Tarth:
Grunting, she came at him, blade whirling, and suddenly it was Jaime struggling to keep steel from skin. One of her slashes raked across his brow, and blood ran down into his right eye. The Others take her, and Riverrun as well! His skills had gone to rust and rot in that bloody dungeon, and the chains were no great help either. His eye closed, his shoulders were going numb from the jarring they'd taken, and his wrists ached from the weight of chains, manacles, and sword. His longsword grew heavier with every blow, and Jaime knew he was not swinging it as quickly as he'd done earlier, nor raising it as high.
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 Mountain's strength was like nothing human. It did not matter. With speed and skill, Jaime could beat them all. But this was a woman. A huge cow of a woman, to be sure, but even so... by rights, she should be the one wearing down.
Instead she forced him back into the brook again, shouting, "Yield! Throw down the sword!"
Not "she's stronger than me because of the malnourishment." No, she goes straight into the Robert Baratheon + Arthur Dayne category.
And then Brienne thinking about it in AFFC...
Brienne remembered her fight with Jaime Lannister in the woods. It had been all that she could do to keep his blade at bay. He was weak from his imprisonment, and chained at the wrists. No knight in the Seven Kingdoms could have stood against him at his full strength, with no chains to hamper him. Jaime had done many wicked things, but the man could fight!
(I also appreciate that Brienne, correctly, doesn't take that as any slight on her own skills. She knows she's good! Jaime's just once-in-a-generation good. No knight in the Seven Kingdoms could have stood against him, etc.)
It's a crime that Jaime couldn't see the melee at Bitterbridge. He would have had SUCH a good time watching Brienne and Loras fight.