I am very unhappy with Files, which replaced Nautilus in 13.04 as the default file manager.
How can I replace it with a better file manager without losing my Personal Folder?
You won't and you do not need to remove it to use another file manager.
Do not know if you can remove it from your system without breaking anything, maybe a better option is to just install another file-manager of your choice and use it instead?
Install another that you might want to use, ie: dolphin, and replace it as your default file handler using
Another good and easy option for that is to edit
this way every time a process calls for Nautilus it will call your new file-manager instead.