If I take a picture with a FF and crop it in Aperture to the same frame size as I would have with a 1.6 ASPC would the resolution /print quality still be the same?
Loosely. Basically, a combination of sharpness, noise, CA, etc. From a similar generation (e.g. 5DII vs. 7D), there's little, if any, difference. Cropping a FF image takes away most of the advantages of the larger sensor. But...if you can live with fewer MP (i.e. you're not making 30x40" prints), there's no downside to cropping the FF image, and a big upside if you don't need to crop.
If your cropping a FF image to APS-C, the IQ will not be what it was unless you are printing or displaying small. It will be somewhat similar to the APS-C image.
Thats why medium format is so popular for very large prints.