For a start, aptitudes command line options are less confusing and more powerful.

Furthermore:

http://superuser.com/questions/93437/aptitude-vs-apt-get-whi...

There doesn't seem to be anything that jumps out as a reason to use aptitude over apt-get there. It mentions that the defaults for upgrading the distro are better for aptitude but doesn't say why or what differences there are.

I can see the search being useful though.

Seeing as my muscle memory is set at apt-get, i'll stick with it for the moment.

There was a brief time when aptitude was smarter than apt-get (it was smart enough to remove auto-installed dependencies when you removed a package, for example). During that time, the advice was to use aptitude instead of apt-get.

Those smarts were later moved to apt itself, but it's still a part of the folklore.

There isn't any specific reason, really. It's a matter of preference, and they can be used interchangeably (which wasn't always the case) nowadays.