There isn't even a comparison between Edey and Shaq other than they're both enormous. Shack was an intimidator with his presence, and was incredibly athletic for his size, with a variety of spin moves to get to the rim for dunks. Edey is more of a finesse player who uses his size for position against smaller, lighter college players, and gets calls if he's touched, while Shaq was literally mugged every time down the floor.
Shaq also played during the tail end of the 'center era', while the game has drastically changed now, making Edey's game pretty much obsolete in the NBA. I see him as a career backup center - he'll make a nice living, but his days as a star end as of next week.