One could probably weave both elements together. Perhaps, it was fated that the two lovers would come from families that hate one another. This could be an approach to take both elements into one thought provoking perspective. Yet, if a choice was forced, I think that the rivalry between the two families is the reason for their deaths. It can become an intensely regressive discussion if we argued this to be fated, but in my mind, Romeo and Juliet are forced to go to ends that bring about their own deaths because of their families' intense hatred for one another. If the families do not hold disdain for one another, the two do not have to go to such extremes, concoct plans where deaths are "faked," and take the risks that they do. One need only see Juliet and the interaction with her parents in Act III, sc. 5 to see the level of intensity that the parents forced upon their children. In the end, the kids had no chance for their love, or their belief in love, to develop. They had to pursue channels outside of their parents, which means that the parents, and not fate were the main reason for their deaths.
It is true that due to the unexplained hatred between the two families, which may or may not be due to fate, Romeo and Juliet are forced to take extreme measures to be together. Therefore, it is the lovers' actions that bring about their eventual deaths. However, it can't be ignored that fate plays more of a part than simply bringing two young people together that are from feuding families. I think it's important to examine the message that went awry toward the end of the play, the message telling Romeo of the Friar's plan and letting him know that Juliet is not really dead. It could be argued that fate was a factor in this message never getting to Romeo. I understand the plague was the driving force in keeping Friar John in Verona due to a quarantine on the city. However, fate can be argued as the cause of this. If that message had safely gotten to Romeo, the Friar's plan could have been successful and Romeo and Juliet could have conceivably lived "happily ever after".