Ask people this question: Do you dust before you vacuum or vacuum before you dust?  You will get a plethora of answers – and different rationalizations for each anwer.
The same goes for baseboards. Should you clean the baseboards before you vacuum or after?
Well, if inquiring minds really want to know, this is what we at Cincinnati Maintenance recommend:
Dust first, then vacuum. Why? Pet hair, dander, dust, and other allergens are are always “floating” in your home, even if you can’t always see them. A good rule of thumb when cleaning is to wipe down your home’s surfaces first  – on a side note, we always recommend using microfiber cloths for dusting and other surface cleaning.  These help trap the particles and allergens in the cloth.
What you don’t want to do is vacuum, then dust, and then watch your surfaces appear dusty once more when the disturbed particles settle once again.
Neither notion of “which comes first” will ensure that all dust in the home is removed, but dusting and cleaning the baseboards first will trap most of the dirt and dust in your microfiber cloths, and then vacuuming afterwards will clean up any remaining debris that fell onto the floor or carpet when you dusted.
So, now you know.