Let's talk both lore and in-game. I haven't tested this out, but does Fiora landing the parry vs Jax e allow Fiora to win the fight? What about post-6 (Fiora's ult is better imo)? Personally I still feel that it's a skill matchup.
Lore-wise, they're both very skilled with weapons, the key difference being Jax has mastered every weapon known, whilst Fiora specializes in sword dueling. There is a youtube video (linked) about a Jax vs. Fiora arena-style fight. FIora wins the first round (it can be assumed because Fiora walks away and Twisted Fate gives Jax a gold card to keep fighting). But Jax, using the gold card, beats Fiora.
In Jax's story, he faces Fiora on a bridge in Demacia, though the outcome is unknown, but at the end of the story, Jax comments that Fiora was finally someone worth fighting. Implying that from first impressions, Jax thinks that Fiora is a challenge.
What do you think?