From a purely hotlapping/qualifying point of view taking the outside line is usually slower. Not to mention the parking lots are usually low grip. There were several incidents where such passes have not been penalised. For example Mark Webber overtaking Lewis around the outside of T1 at Hockenheim last year (at the start) etc.
The only advantage I can think of that you get by taking an outside line is if there's a 1st corner tangle, then you drive around that tangle by going around the outside
Btw, for those who are on BBC's feed, even if you're not watching on the BBC, I never realized how much Legard digressed, funny as that is. Martin Brundle talks about the race, while Legard talks about things happening off-track. Not to mention he gets inside/outside messed up, and also front/rear wings (amazingly

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Btw, here's my take on the situation. (This is my first time doing a frame by frame analysis, so please be nice

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Vettel takes a wider line on entry to Turn 3

Vettel cuts back underneath Button to get a better exit from turn 3

By the entry of turn 4, Vettel is ahead of Button

When Button is on the apex of 4, Vettel is ahead:

Button leaves the apex, and Vettel hits the exit kerb of 4. Vettel is clearly much ahead here.

Here is when Vettel's car leaves the track

So for all intents and purposes, the pass was over and done with by the time he left the exit.