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.)
I really like the original Deus Ex.
EXP is given for completing quest objectives and exploration, not for killing enemies or using skills.
Players will do things that give a reward. I have tried role playing some games, but most of the time I ended up doing things this way because it gave the best reward.
Deus Ex rewarded players for doing quest objectives and exploring the environment.
Most RPG reward players for killing as much things as possible, so your main char is a psycho killer.
One thing I really dislike is when the most rewarding way to play is to do all quests first and then kill everybody before you go to the next area.
Like you save the village from a monster attack and save some kids from a dungen and after you get a reward for it you kill all villagers.
PS:
Playing as psycho killer can be an option in games.
My point is NOT that I am against certain playstyles.
My point is that one playstyle should not get better rewards than others, at least on average over the whole game.
If you have the quest to save villagers, you should get less or even no reward if you kill some of them.
If you have the quest to kill all villagers, you should get less or no reward if some of them escape alife.
If you have both quest you have to chose which one you follow. If you kill some of them and save some others, both quest givers will give you no or little reward. If you save them first and kill them later both quest givers will be angry, give no reward and will never give you a quest again because you are completely nuts and unreliable.
Prof. Dr. Dr. Mad S. Tist 
