The linked blog post [1] contains a benchmark against the Canterbury Corpus [2]. It is hard to test against other compressors because of its very low memory requirement, but LZO1X-1(11) (`lzo1x -11` in LZBench [3]) comes close as both LZO1X-1(11) and HS 13,4 targets 8 KB of work memory. The result (higher is better):
It does seem to have a good compression compared with LZO1X. I think this is mostly because LZO1X has a requirement that literals should be aligned at byte boundary for the performance but Heatshrink doesn't.