Of Mares and Magic is damn close to what you are suggesting (Trixie learns that the only functional difference between her and Twilight in terms of schooling and skill is that Twilight caught the eye of the Princess and Trixie did not, so she returns and challenges Twilight to a magic duel to settle the matter), but that is a Twixie story anyways so I suppose it doesn't count. If it wasn't, though, I would say it would be almost exactly like what you are talking about.
I know I've read a couple where they've tried to learn from each other, but I can't recall exactly what they were about (so it may have been the B-Plot of the story).
Almost there, in fact is the premise of
"Rivals" for both characters(Twilight and Trixie), I was thinking about that story, but it doesn't meet the criteria that I constructed from the ending from the episode, I've to see a fanfic that fulfil this aspect without resorting to additional backstory or additional previous events, something that can be done.
In second thoughts, It depends more on personal interpretation of the episode than general consensus, so I guess that you could be right in "closest" terms, however I do believe that the relation between is has more tendencies towards "conflict" than "shipping".
Also, you got it right in the last post.
CoffeeGrunt
As far as similarities, I personally don't believe Trixie has any practical magic potential. Her ability seems to be visual magic rather than powerful magic like Twilight. As a result, I don't feel that they're a great match for each other in terms of magical wizard-offs.
That was my initial thought, however the ending of the episode is open to interpretation, something that can be exploited, Trixie on wizard-offs is possible as long as the background and development suggest this, in "
realistic" terms Trixie is a show off, but a good support to her can be build parting from the events of
Boast Busters (fanfictionally speaking).
I'm aware that both posts sounds a bit contradictory but bare with me, they aren't(somehow, creating a backstory from the events of
Boast Busters, not prior to them).