Aster versus Fleabane

I took this photo last July. A friend who was getting a little confused about how to tell if a flower was an Aster of a Fleabane held these two examples and asked if I'd take a photo for her. It's telling what kind of Aster I come across that becomes a real problem for me - there are so many different kinds growing in the wild. Oh, by the way, the smaller, purple flower is the Aster. The Fleabane has much narrower petals and many more of them. To get a completely accurate ID, of course, one needs to look at the whole plant.