I took 3 test files and ZIPped them. With the 3 test files again I RARred them. Each .RAR archive is smaller than the corresponding .ZIP archive.
Does the RAR compression algorithm give a better compression ratio than the ZIP compression algorithm?
Although it depends on what you're compressing, I've noticed that RAR often does get a slightly better compression ratio (although I usually don't find it to be too significant), but the data I need to compress is likely very different from the data you need to compress.
If you run any benchmarks of your own, be sure to include 7-Zip in the list of contenders as well since it's definitely a worthwhile cross-platform alternative that can also handle the .ZIP and .RAR formats seamlessly:
7-Zip (free and open source)
Also, here's a document that examines compression ratios between various compression archiver tools, which I believe you'll find interesting:
The 7-Zip .7z format gives best results overall, and also has much stronger encryption than the .zip format.
Please recall that the .zip format is actually two DIFFERENT formats:
Many tools, such as the zip support built into some versions of Windows, only support the older zip format.
Additionally, the zip format has really weak encryption that is easily cracked. The RAR and 7z formats are both dramatically better than the old style zip encryption (I am not versed in the quality of new zip compression, so cannot comment on it).
7z is a great choice. RAR is also a good choice.