1.3 is the last version made by Redigit, the original creator of the game, in 2010. It has an outdated editor and fewer features than later versions, but can be supplemented with the PGE editor.
1.3.0.1 is a modification of 1.3's .exe with a few replaced graphics and resampled music. It's identical to 1.3 feature-wise.
1.3.0.2 is 1.3.0.1 with LunaLua built in. I recommend playing this version if you want to play 1.3.
2.0 (now officially known as SMBX2) is a continuation of the SMBX project by the SMBX2 development team from talkhaus. It has the PGE editor built in and numerous new features. It is in beta currently, and when it is released it will almost certainly become the main version since it will have the most content and is open source (and Beta 3 is already sort of the main version on this site). SMBX2 is fully compatible with 1.3 content, as it is built on top of 1.3.
1.4.x, also known as SMBX 38A, is a clone of SMBX with additional features created by the developer 5438A38A. It is not actually a new version of SMBX, but rather a clone that closely but not completely accurately emulates its features and mechanics, so it is not compatible with 1.3 or 2.0 content.
Source!