Hi,

I dont shoot makeup but i do I do shoot my girls a lot and I own both lenses. 

Look at the minimum focus distance of both lenses. The 70-200 cannot focus on anything closer than 47" away, measured from the camera's sensor, not from the end of the lens. The lens is 8" long, and the sensor is about an inch inside the camera so, roughly, you can take pictures with the end of lens just about 3 feet from your subject. That is pretty darn close.  The lens has great resolution so you should be able to crop the image to enlarge the image to where you want it. 

The macro has true 1:1 close focus ability so you could shoot an extreme closeup and get an in focus shot of a patch of your model's skin the same size as the sensor in the camera, which would be displayed blown up to the size of your monitor. Not sure an extreme closeup of pores and hairs like this would show off your makeup work to its best advantage.  Very possibly overkill on the closeup ability. 

The 70-200 gives a lot of flexibility. It can not only go 2x as long but also 1/3 wider than the fixed 100mm.   100mm can be very long at times, especially on a crop body. 

What camera era do you use?