What's easier or more cost effective would all depend on what kind of equipment you have access to, what sort of disposal site you have access to/or not, and what future plans for the area are. If you're going to plant another tree grindings would be good I would think, if it's going to be returned to lawn I would think you'd want soil. Just my .02.
If I was replanting a tree, I would put soil in there. Whatever was most similar to the soil that is in the rest of the yard. Trees are used to growing in a forest setting where the top few inches are mulch (wood chips) but not 2 feet down.