madara said that the sharingan have to be together in order for it to get stronger. if obito wasnt there to see rin die, then they both would have never awakened the mangekyo. and i believe the reason why kakashi fainted was because his body wasnt able to withstand the strength of ms yet. obito was able to master and use it quickly because he had senju dna. as we all know, senju dna enchances the sharingan which pretty much explains how madara got his rinnegan after his fight with hashi.
mastered/powerful sharingan + senju dna = rinnegan
as for kakashi not using his ms til shippuden, i think kakashi have awakened it when rin died but he wasnt able to use it until shippuden because he wasnt stronger.
for example, kakashi was able to use kamui only two times at the beginning of shippuden and now he was able to use it more than 4 times when fighting obito. it seems that the more kakashi gets stronger the more he is able to strengthen his sharingan. so in this case, obito had the advantage whereas he is a pure uchiha and he has senju dna and kakashi has the disadvantage bc he has neither dna