The two versions DO conflict with each other. What you need to do is disable cloud saving on the steam side to keep any progress made in the itch version from being overridden.
Viewing post in Update 1.3.0 (re-upload) comments
Gotcha, thnx bro. Purging everything seems to have worked. I downloaded just the itch.io version and it seems have have let me save last night, when i boot it up again tonight ill know for sure. I lost everything in my museum but like i said thats fine. I really enjoy playing the game. On the steam version for some reason it was like i was invincible, no matter the difficulty i always recieved only 1 or 2 damage. With the itch.io version i actually feel the correct damage which makes the game more enjoyable. Not sure if it was a bug from steam or from the last game version.