apt-rpm is another tool that is basically the same as apt-get but deals with RPM packages. Yum and apt-get are both package management tools. If you want to get real technical, apt-get is primarily a Debian package management tool. It serves as the gateway between dpkg (the actual program that operates on the package files) and the online repository of packages.
Whichever one you choose to use for package management, use only one but not both at the same time. Not litterally simultaneously, I mean one today, the other tomorrow kind of thing. Doing so would just confuse each system and probably mess up your dependency tree, software may be overlapped or add/removed unpredictably.
As far as which to choose, it's really up to your personal preference.