To put it simply, Debian's packaging system in comparison with Red Hat's is like comparing the Empire State Building with a crumbling shack in a downtown slum. ;-)
One of the primary reasons, is that Debian packages all[*] come from Debian. Red Hat packages are created by third parties as often, if not more so, than by Red Hat. This means that there is a much lower level of quality control among Red Hat packages, and a much greater variation in quality.
Secondly, there is a difference in how dependancies work. In Red Hat, packages are dependant on specific files. In Debian, packages are only dependant on other packages. This makes them, in my experience, more reliable. They won't break because a single file may have been moved.
Also, Debian has a reputation, and actively works to maintian it, for stability and reliability. It may not always be cutting edge (Assuming that you are using 'stable'. If you use 'unstable', which is still as stable as most other distro's stable in my opinion, you may occasionally run into problems) but it will be rock solid.
My first distribution was Red Hat, and I tried out a number of others early on, but ever since I installed Debian, I've never felt like I was missing anything. Once you try apt, you'll never want to give it up. ;-)
I'll take some time when I get home tonight to talk more about Debian, and prolly put it in a journal entry. Or, feel free to talk to me online, and I can tell you 'bout it, or answer any questions. An intersting thing to note, though, is that among the SorceryNet 'staff' people who run Linux, more of them run Debian than anything else. ;-)
[*] Debian has an open policy that allows just about anyone to become a package maintainer. When this happens, they get some training, mentoring, practice, and become a Debian developer. This ensures higher quality packages, better testing, and allows you to get all packages from a single source.