How does image quality of scanned photo prints compare with prints copied with a digital camera?

If you are starting with the print you are already at a disadvantage because of the dynamic range issues which are not directly related to the resolution (most scanners do not have enough sensitivity to capture both shadows and highlights). The best way to make a digital copy from an older photo is to start with a transparent negative or a slide - many labs have equipment to scan these (do not use regular scanner, even with a "slide" attachment!)
If you are limited to a printed photo a quality scanner will be easier to operate then a camera, but with some effort results will be comparable.
With the camera you have to ensure that plane of camera is parallel to the photo, stop down the lens to make sure everything in focus, and provide uniform lighting without color cast. Scanner takes care of all of that.

well, it depends on your scanner. I find that digital using a digital camera is superior, and you don't need to scan. Most have a USB cable you can plub directly into your computer or printer. My printer even takes the memory cards for most cameras.

place your photo in the scanner and press scan