The Mushmen version has additional locations in the wilderness and some mechanics that require many days to pass in game before you can enter the dungeon.
The Cairn version (here) has an updated dungeon design for better crawling and allows the players to access the dungeon from Day One (if they can reach the entrance). I think i would recommend the Cairn version for Shadowdark. (You'll need to convert the stat blocks either way, of course.)