Circular breathing is easiest to accomplish on the didgeridoo. This is because of several reasons: optimal back-pressure (hits the sweet spot between lack of resistance on a flute and too much of it on an oboe, for example), loose embouchure (relaxed lips make it easier to puff up the cheeks) and single drone focus (no distracting fingerings required).

I also suspect the intense vibrations have a similar effect (probably stronger) to humming, which is known to dramatically (15-20x) increase the release of beneficial nitrous oxide in the nasal passages.