I would think being a RedHat derivative would make it less popular, not more popular.
CentOS accounts for about 80% of Virtualmin installations. Your disdain for Red Hat seems to not be widespread. 
I can also tell you I don’t like the fact that Debian is almost dead last when it comes to implementing the latest software/GUI updates.
I’m not sure I agree with you on this count. GUI isn’t the core focus of the Debian project (while it is of Ubuntu), and it shows. But, that has no bearing on how good, or how well-maintained, it is for server usage.
I would choose Debian over Ubuntu for servers at this point in time.
But, we use CentOS on our world-facing servers, both because it is what most of our customers are using, and because it has a very good history for stability and security. Debian and Ubuntu occasionally break things (mod_php, for example, is the latest victim of that, getting automatically removed when upgrading other components).
As a comfortable Debian (and Ubuntu/Kubuntu) user, what major things would I find to be different in CentOS (other than the obvious package/installation methods)?
We tend to recommend folks use what they are comfortable with from amongst the Grade A supported operating systems. If you are familiar with Debian, use it. It works great. I have a few little complaints, but mostly I think either CentOS or Debian are great choices (certainly superior to the Grade B, C, and other systems that either have really short lifecycle like Fedora, or have piss poor package management like Solaris or FreeBSD).
CentOS is, in my experience, a wee bit more predictable than Debian. Breakage is less common, as the package version policy is more strictly enforced in CentOS/RHEL than in Debian or Ubuntu. Ubuntu, even in the LTS version, seems to be the worst amongst these three systems. They actually changed a configuration file option name for saslauthd a couple of months back; breaking existing installations. That was just stupid and pointless.
It’s possible to break any of them, and there is a tendency among new users to CentOS to enable a bunch of third party repositories without understanding the impact of such a decision (enabling a third party yum repo is effectively granting a third party root access to your system, and should be done with extreme caution). Third party repos also don’t generally have the same packaging policies and QC requirements that CentOS/RHEL core packages have…and so, if coming from Debian you find yourself wanting that huge array of available software found in the apt repositories, you might make bad decisions in order to get that feeling of having everything under the sun available for instant installation.
Anyway, I think you can expect CentOS to be at least as stable as Debian STABLE. But, nobody is encouraging you to use a new system, if you’re already comfortable with Debian.