First of all, both of these foods have funny names. A dough-nut? Well the dough part I understand but nut? That makes no sense.
In Spanish, factura also means “bill” as in your telephone bill.
So why these two foods came to signify a doughy, sweet, breakfast food is beyond me. However, this has nothing to do with their qualitative differences.
Let us examine the flavor profiles of these two yummy food. Yes, let me reiterate here at the top, that they are both yummy and delicious foods. The well made medialuna (the Argentine croissant) really has nothing on the glazed donut and vice versa. They are two different styles. The medialuna is much lighter and baked and the donut is fried. There you have the primary difference.
I also feel that donuts are much sweeter than facturas in general. Here is where I am partial to donuts, especially the maple bar and the apple fritter. They have a sweetness that satisfies a craving. When getting medialunas or other facturas, I find I really have to look for the right ones in order to satisfy my sweet craving. Occasionally you will find the panaderia that has apple flavored facturas, and quince paste on facturas is ubiquitous, but they put so little on! It’s only ever one bite worth.
I also find that there are many more facturas that are made badly than donuts. Very frequently facturas will be dry, old or poorly made, where I almost never have a problem with a donut.
In terms of cost as well, I find it phenomenal that a dozen donuts costs the same, dollar for dollar as a dozen medialunas. In Argentina, a dozen medialunas is around 20 pesos, or 5 dollars, and in the US the price of a dozen donuts is about the same, unless they are all massive apple fritters (which are really like two donuts).
I’m sure Fernando and I will debate this on BA Cast: The Buenos Aires Podcast soon.