Boy Howdy is there ever a difference in the cheeses! Even between quality domestic brands and the mass produced stuff. Imports just step up from there, and keep stepping up.
DW and I got the chance to to a taste test, and we selected Parmesan as the item to test. We purchased four different ones: ALDI's Wisconsin brick Parmesan which is supposed to be a step up from their regular brick, Whole Foods Wisconsin Brick (labeled as a high quality cheese, recommended by the fellow working that department, and the most expensive of the Wisconsin Parmesans), Whole Foods Imported European Brick, and Whole Foods Italian Brick.
Those are ordered according to price, cheapest to most expensive. And ALDI or Whole Foods are not their brand but where we bought them. All were small 1/2lb bricks as that is all we could afford... and barely at that! I liked the Imported European over the Imported Italian myself, ALDI wasn't even close.
Think of it like this: Eat a slice of quality brick cheese then eat some cheese food slices made with oil not milk. You get the picture...
On a day to day regular basis I would probably buy the Wisconsin Parmesan from Whole Foods at $4.45 for the 1/2lb, and the Imported European for special occasions at $9.87 for the 1/2lb.
I will of course look around for other places that may carry the same quality stuff at lower prices. I would be happy to hear from others on what they think of the prices.
We also got the chance to try Water Buffalo Mozzarella and WOW. We made the 'traditional' Italian Pizza using flatbread, tomato slices, the WB Mozzerella slices, and plenty of fresh green basil.
All this to basically say, yes use the best quality cheeses you can afford in your Alfredo sauce, and I also advocate the fresh garlic.