Question: I was just wondering, what's the difference between these file formats? Shouldn't there be just one or two that generally tend to perform superior to most others?

Answer: 
If its linux based, .tar.gz or .tar.bz - otherwise known as your humble tarball. In windows, .zip - natively supported since windows XP. You also often encounter .rar (especially with files from slightly dubious sources) and .7z (windows/open source software most often).

If you want to be ABSOLUTELY sure your file will be opened by most modern OSes (and some not so modern ones), .zip is the safe choice. 

Efficiency depends on the filetype in many cases - for example lrzip works best with VERY large files, text files always compress very well, but compressed audio dosen't, and compression ratio is often traded off for processor and ram usage- as such, there is no 'best' file format for compression
While `.z` is the oldest, as old as Unix, the most prevalent compression format is `.zip` because it is the only format supported natively by all versions and flavors of Windows since Windows 98.