"Cutting" vs "sanding" hardwoods

[Eliot M.]

Is there a difference between "cutting" and "sanding" hardwoods, and if so, which one would you go with, and why? I had a contractor walk through the house the other day and said that he would "cut" my particular hardwoods down about an 1/8th of an inch, as opposed to sanding them. He said cutting would bring the floors out much better than sanding, and that the cutting would be $3.25/sqft as opposed to sanding which would be $1.50/sqft. That's a huge difference and I'm wondering if anybody has had this experience?