Advantages and disadvantages. The Alaska mill/chainsaw is not as efficient, but a lot less expensive and will go where no band saw can go.
The good band saw mills need water cooling and are not cheap.
The Chainsaw mills can mill it where it falls, then you just haul the boards out of the woods. Great if you don't have heavy equipment, or access with heavy equipment (across septic fields, etc).
So it depends on your volume, your access, and how deep your pockets are.
I know of a guy who set up a nice 24' long water cooled band saw mill ... and he has not milled as much wood as I have!