I was fortunate to visit both properties in 1988.
I can't disagree with most of the sentiments expressed earlier.
I, too, felt that the Cascades course was the golfing highlight although the Old White was an endearing course as well (too bad we played it in a constant rain). I didn't mind the Greenbrier course as much as others here but the 3rd course (Lakeside then), wasn't overly special, although probably a good track for beginners or the higher handicap player. I did play the Lower Cascades course also and remember it as okay with very quick greens.
We stayed at Greenbrier and must concur that the amenities are special, especially the cuisine! Too bad that it's so stiflingly formal! Really, a jacket and tie to see a movie or have a beer!
While we were at the Cascades, we stayed at the Cascades Lodge, a baby sister to the Homestead itself. Although we just wandered around the Homestead, my general impression was that the Greenbrier would have been the superior facility.
Take Ben's advice... visit both for three days and draw your own conclusions.