Full game doesn't crash, doesn't give you the browser scroll function on middle click (the shortcut to pick a color of an existing building), ability to export as STL, no full game links, ability to create oversized screenshots, some settings. The full game isn't deterministically equal to the browser one (roofs slope in different directions sometimes, decorations in different places). It should also run slightly better, although both are pretty lightweight.

Notably, the export strings are the same.

Basically: you're not missing anything from the core experience, but the browser version is slightly inferior. And buying the full version helps Oskar make more neat stuff in the future.

Edit: it's also a smaller build area.

What makes you think it's a demo?