Do you intend to print this on uncoated paper, because the .ai swatches are Pantone Spots and the have the U suffix which indicates uncoated paper. The new versions of Indesign have more accurate display of Pantone spots and the U versions of the spots are being displayed muted which is what would happen if they were printed as spot colors on uncoated paper.
So here's the difference between Pantone U and Pantone C:
Using spot colors is the problem if you convert them out of InDesign you will get muted colors because of the U swatches. So if you want the color you are seeing in AI, double-click the swatches and convert them to Process in AI.