More than most people expect. Gut microbes are still active in the stool sample after it leaves the body, so a kit that does not stabilise DNA in transit can allow oxygen-tolerant bacteria like E. coli to keep growing and strictly anaerobic commensal bacteria to die off.
Microba's collection device has been assessed in published, peer-reviewed research on preserving faecal samples for metagenomic analysis and demonstrated it accurately preserves the microbial community at temperatures up to 50C for at least four weeks. If you are comparing tests, it is a fair question to ask: has the preservation method been validated and published?