One downfall to follow-me eyes that I never really thought much of until I read about it, is that it photographs very differently than toony eyes. Follow-me eyes will always appear to be looking at the camera. So some situations or poses don't actually work all that well for it.
Take, for example, two suits bumping noses (both their sides are to the camera). Fixed toony eyes will work best for something like this, so it looks like the characters are actually looking at each other. With follow-me eyes, it'll look like both characters are awkwardly glancing at the camera through the corners of their eyes.
Same goes for any situation where you want the character to actually be looking directly at some object. The audience or camera will perceive the character as actually looking at said object with toony (or other static) eyes. With follow-me eyes, the character will appear to be facing the object, but still be perceived as staring at the audience or camera.
Just something else to keep in mind when choosing between those eye styles. Do you really want the character to always appear to be staring at the audience, no matter where they are facing?