Here's a simple exploration of scanning a print. A bit long but its mostly images. Rather than compare a print from a scan to the original print, I compared the scan of a print from a image to the original image, in this case a grayscale ISO 12233 test chart in jpg format. Color adds another dimension that I decided to skip. You can try something similar to see how your scanner and software behave.
Here's the original image, the image with clipping highlighted, and a 1-1 for later comparisons. Note the histogram - the dark border (not black) is the spike towards the left, and the hump in middle is a result of the antialiasing for text and lines. The 1-1 shows a fine diagonal line in the center of the rings.
I printed from LR to a Canon MP640 on both high gloss photo paper and matte paper to show how different surfaces affect printing and scanning. I scanned on both the MP640 and Epson V750 at 300dpi, 600dpi, and 1200dpi in VueScan. The resulting DNGs were 25MB, 101MB, and 404MB. The JPGs were about 7MB, 26MB, and 94MB, varying a bit . I also did a 2400dpi scan for yucks, 1.6GB.
Using VueScan allowed me to compare scanners since I used the same settings for both. There was little/no difference in scans between the MP640 and the V750 so I'll just show the MP640 here. Today most scanners are capable of high quality scans from prints. In my experience, the big difference is the film handling capabilities which is where the V750 shines for me.
First let's look at the scans from the glossy and matte paper at 300, 600, and 1200. The printing and scanning process converts from digital to analog and back so we expect some loss and noise in the process. Note these images all capture the faint diagonal line in the center of the rings. The matte paper produced results similar to faded 100 year old photos I've scanned. It also shows the affect of a different surface which absorbs and bleeds more than the high gloss.
I also downsampled the 600dpi and 1200dpi scans to 300dpi in VueScan for a more direct comparison. Heres to 300, 600/2 and 1200/4 scans in glossy and matte. From these scans it appears the additional scan resolution didn't gain anything noticeable after they were normalized to the same resolution. It also didn't seem to matter whether VueScan or LR did the downsampling.
A quick check of the histograms on the 300dpi scans showed the glossy scan was close to the original, the matte scan not so much. The histograms were consistent across different resolutions for the same type of paper. Here's the original, gloss, and matte histograms.
A little correction to the gloss and matte scans in post can get the historgrams close to the original image with similar clipping. You could do something more elaborate, but PP wasn't the point of this post.
And the resulting 1-1s - original, gloss, and matte. The gloss is image is pretty close, the matte image less so.
Overall I'd say the scanners and software did a pretty good job with the round trip comparison. The difference in quality was largely the paper in this case.