If APT fails catastrophically, your complete system could be in limbo. If Homebrew fails catastrophically (which never happened to me), the rest of your system is fine, you wipe out /usr/local and are up and running again in a couple of minutes (since most large packages are bottled).
By the way, aptitude does not really help you in the typical error case: a package (continuously) fails in dpkg-reconfigure, which causes the complete install/upgrade to fail.
Home brew, when things go wrong, goes wrong disastrously in my experience. You're never quite sure where you're left, and you have to spend a fair bit of time picking through what actually failed.