I think that an extended final is much better overall for the players and spectators so long as both 1st and 2nd place get paid and the difference between the payouts isn't very large relative to the total payout.
The way I see it, the primary goal of the double elimination format is to get the two players that play the best throughout the tournament playing in the finals. Assuming that the better player wins every match, that will be the case. Of course, it doesn't usually work that way since the sets are short and a player often falls victim to bad rolls or an uncharacteristically good game against a weaker player, but that's another argument.
Once you have the two best/luckiest/whatever players in the finals and they are both getting paid, why not just have them play one long match for the difference between first and second and bragging rights?
Going through either side of the bracket to the finals requires lots of good play and a bit of luck, so who cares who had the tougher road or played better on the way there? The winner's side finalist might have been the one to put the other player on the loser's side, but they might not. If the winner's side finalist really is the better player, shouldn't they be even more confident about winning a longer race? If they aren't, doesn't that mean that someone just got a lucky win along the way?
In any case, I say that once you're down to two players, let them go at it without giving one an advantage based on how they got there. If the race is longer, the better player is favored by even more, so that seems plenty fair to me.