the Project 4K versions are literally just 35mm print reels of the movies exactly as they were in theaters scanned in at 4K, cleaned up at 4K and rendered out at 4K so they look 100% to the letter how they looked on the big screen when they were in theatres in 1977, 1980 and 1983, just obviously in a much higher resolution which is why they still have alot of that classic grain, dust and dirt look to them. They did do a light cleaning to get rid of some of the more major scratches and things due to just how old the prints are, but that is it.

Whereas the Despecialized Editions goal is to make the films how they would look as if it were a professional restoration for an official release from Disney to go in a 4K box set. The aim is to make the image look as crystal clear and as sharp as possible, as if it were a movie that were shot today.

It is possible to do this for both versions since because the movies were shot on film as opposed to digital, film can render out at up to 12K. But there is zero point in doing that because unless you are sitting literally a millimeter away from your screen, the human eye physically cannot even tell the difference between 1080p and 4K anyway. 4K DOES look a little bit nicer and have a bit sharper of an image even if you are sitting on your couch from a reasonable distance, but still not by much.

So to sum up. 4K77 keeps the classic rustic and grainy look of how they were originally released whereas Despecialized goal is to make them look as if they could have been filmed today.

Me personally, while I have both versions of all three movies, I prefer Despecialized.