UE4 Linux: This project was made with a different version of the UE

I ran into the same thing, I think a project can only be compiled for one OS at a time.

If you are using version control (eg. git), it might work better to have one main repo for your project, and a clone for each OS you want to develop on if you have the space. Then you can push any changes back to the main repo and pull them to the other OS as needed.