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.
As a connoisseur of monad explanations (if not monad understanding) Crockford's talk sounds rushed. It spends a fair amount of time on setup, but when it gets to the meaty bits, it has the feeling of glossing over the details. It could be that all the essential elements are there, but they're covered to quickly to impart any comprehension.