Some would immediately answer "neither". You may be one of them, but you might still be interested in this question because how others answer it may affect you anyway.
For others, this seems like a false choice. Why is it even a question? Why can't it be both? Again, this distinction may not apply to you but if you are someone who would choose "both", you may be especially interested in those who emphasize or only select one answer over the other.
But where does such a question come from anyway? And what do we do with it? What does it mean, for example, when someone labels herself or himself as a "follower of Jesus" as opposed to a "Christian"?