Flooring Tile - Gap Between Tile and Front Door Threshold

I was just wondering what is normally used to fill the gap between tile and the threshold. As part of the warranty work on my new house, I had the original threshold replaced. There was originally grout between the tile and the threshold. Of course, the grout fell apart while the threshold was being removed. Now I have the option of having grout put back into the gap or colored caulk. I was told that colored caulk is what is supposed to go in that gap. Is that true?

I would go with the caulking as there is going to be some movement in the threshold. The grout will crack and probably not stick to the threshold.