I think the xp should based upon the length of time it takes to get the same objective. The quick way vs the long way.
No, exp should be given depending on the outcome of a quest, not how you get there.
Of course, how you do it can change the outcome and it might influence later quests.
If I take your words literally,
speed runners would profit most from this and think this is not how an RPG should be. (I don´t think you mean it that way.)