apt-get is a command-line package handling utility while aptitude is a high-level interface to the package manager. There isn’t much difference between the two except aptitude will remove unused package dependencies automatically whereas with apt-get you have to do it manually. Neither removes dependencies as that would cause problems. Dependencies are packages that are depended on by other packages. You don’t want to remove them.
To remove unused packages with apt-get use
sudo apt-get autoremove
With aptitude there is nothing to do as it’s automatic.