As a casual user myself (at least when it comes to archive utilities :P ), I've only encountered the RAR, Zip, and 7z formats in everyday use. Those three are, by far, the most common formats around. You might have to extract an ISO every now and then, and perhaps even a tar.gz archive. All of which are supported by both WinRAR and PeaZip. Unless you're a developer or something, you're not going to be seeing anything else. And if you're a developer, you sure don't need to be following any of my advice.
For most people, the main difference between PeaZip and WinRAR is the fact that one is open-source, with a pretty GUI. And the other one is proprietary, and rather ugly.