Arjan provides a quick overview of data compression, tests with the venerable zlib at different levels, XZ compression results on Ubuntu vs. Clear Linux, bzip2 results, and LZ4 and Snappy. He concluded his Clear Linux blog post with:
zlib is a reasonable "middle of the road" algorithm or implementation that reaches reasonable compression at reasonable CPU utilization, with the ubiquitousness and internet standardization as added benefits. When needing maximum compression ratios, xz is the clear choice at the expense of longer compression times, while both LZ4 and snappy provide interesting design points at the high performance and throughput end of the spectrum. The bzip2 algorithm is likely only interesting in more niche usages where the data is known to have bzip2-friendly patterns.
Those wishing to check out this first Linux data compression comparison of 2017 can find all of the data and commentary at ClearLinux.org.