The primary advantage is that a 3D printer is truly able to create features in any orientation in 3D while a typical mill cannot. The price of consumables isn't really something I consider important, especially when prototyping.
The thing that a lot of people don't realize about traditional machining operations is just how long they take to set up. I didn't, myself, until I bought a CNC mill. I thought it was just a matter of sticking a big hunk of metal in it, hitting Go and then coming back when it's done.
The first problem is that for a typical 3D axis milling machine you have to find a way to mount the material you intend to cut without getting in the way of the cutter, and if your part is at all complex this can be very tricky. Different materials and thicknesses all require different methods of mounting, and learning how to mount and setup a part is an education in itself.
The second problem is that a 3 axis mill can really only cut down. That means if you want a hole in the up/down Z axis, you are fine. If you want one in the X/Y axes you are out of luck. You have to finish your Z axis operations, unmount the part, turn it, find a new way to mount it, zero the machine to the new part configuration and then do more operations. If you have a part that has, for instance, mounting holes on several sides you are looking at a LOT of manual work to complete that part. And each time you remount the part you have to be able to tell the machine exactly how the part is mounted so that everything lines up.
Industrial machine shops get around this by using 5 or more axis mills. These are insanely expensive and not really available to the home / hobby engineer, although I am quite interested in what http://www.pocketnc.com/ is doing.
3D printers, on the other hand, are truly 3D. You can have features in almost any configuration and it's no more difficult to print than a simple cube. It is literally a matter of starting it up and coming back when it's done.
I don't think 3D printing is the be all end all of machining, especially FFF, but for the home or hobby engineer it's an incredibly powerful and easy to use technology right now.