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
I prefer compressing my data using \*.rar with WinRAR as it is completely customizable. I use it because I can choose how much I want to compress it and I can set passwords to protect my archive. If I'm doing something involving disk images, I'll compress to \*.iso or \*.daa using PowerISO. 

Whenever I'm not on one of my own computers, I compress it using Windows 7's built-in \*.zip compressor. On Ubuntu, I will probably compress in \*.tar.gz or \*.zip.