If what you want is to compare object disregarding the way the code is formatted, then you do not need beautifier. The code has to be parsed and compared syntactically and not as text. Beautifier does much more (it parses and formats, which means at least one huge step that does not help in comparison results). There's also at least one more thing - code that is syntactically equal, does not have to be identical after beautification (if beautifier is configured to preserve some formatting features of original code).
To summarise: I believe that what you need is syntactical code comparison, not text comparison of beautified code.
Code beautification may be beneficial for presenting code differences, but that's another thing.
