Currently, there's no difference between the itch.io and Steam versions of the game, apart from Steam-native features like Steam workshop for mod support and Steam achievements. If we end up making any patches that would cause the two versions to be different from each other, we'll make an announcement about it.
You can switch between versions without losing your progress -- in fact, you don't even need to take any extra steps to "transfer your progress," as both versions of the game write data to (and read data from) the same folder (located in %appdata% if you're on Windows). If you install a different version of the game, when you launch the game it should locate your old save file and automatically pick up right where you left off.