The biggest advantage is when removing packages; its dependency resolution is (supposedly) much better so it's able to find and remove orphan packages more accurately without hosing your system.

It's also got a much friendlier set of commands:

  $ apt-get upgrade vim # aptitude upgrade vim

  $ apt-get dist-upgrade # aptitude full-upgrade

  $ apt-cache search # aptitude search

  $ apt-get install --reinstall vim # aptitude reinstall vim

  $ apt-get remove --purge vim # aptitude purge vim

The list goes on.

It's also got an awesome ncurses based interactive interface if you just type:

  $ aptitude

Great for sysadmins who miss synaptic or anyone who feels like a GUI is just too mainstream.

Aptitude has an optional screen-oriented GUI, much better search and filtering capabilities, a listing of "new" packages each time you update, and an excellent dependency resolver.

My favourite feature is the search capabilities, which are well integrated and extremely powerful.

    # installed packages with yaml in the name
    aptitude search '~i yaml'

    # installed packages requiring yaml
    # (~D means depends on)
    aptitude search '~i ~D yaml'

    # packages whose name starts with lib and
    # mentioning SQL in their descriptions
    aptitude search '^lib ~d sql'

    # installed packages from some non-standard repo
    # apt-cache policy describes package origins
    aptitude search '~i ?origin(apt.opscode.com)'

    # why is libvirt0 installed?
    aptitude why libvirt0

    # which ubuntu metapackage is keeping libvirt0 installed?
    aptitude why '~i ubun' libvirt0 

    # don't keep any transitional package installed
    sudo aptitude markauto '~i ~d transitional'

    # purge ganeti packages
    sudo aptitude purge '~i ganeti'