In terms of pattern shape, I think of a supercardioid as being a one step away from cardioid (tigher in front) with a relatively small reverse-polarity rear lobe. I think of a hypercardioid as being one step away from figure 8 (wider in front) with a somewhat larger reverse-polarity lobe.
However, assuming both sound equally good on their own terms, and that both are well behaved with their patterns remaining well defined across the full frequency range of intrest (two large assumptions!) the defining differences for me in choosing one over the other are three-
1) Where the cancellation nulls point (the specific directions in which the microphone is least sensitive)- for a supercard that's somewhere around 125 degrees off-axis, for a hypercardioid it's more like 110 degrees, whereas it's 90 degrees for an 8, and 180 degrees for a cardioid.
2) How even the difference in sensitivity is on average across the entire back hemisphere. A Supercardioid has a more even distribution across the back hemisphere in aggregate than a cardioid or hypercardioid. In that way it is somewhat akin to a subcardioid in terms of its collective overall off-axis behavior, even though it is a far tighter, forward-biased pattern. It provides high on-axis sensitivity with the most even off-axis sensitivity across the rear hemisphere.
3) Hypercardioid maximizes the directivity coefficient above all else, which is the difference in sensitivity between sound arriving on-axis (directly ahead) verses sound arriving from all other directions in aggregate. It provides the maximum forward sensitivity possible, but at the cost of a rear facing hot-spot which makes for decidedly more pickup from directly behind the microphone than a supercardioid.
Sennheiser's choice of a supercarioid pattern which lies partway between a traditional supercardioid and hypercardioid, so that it provides the same -9.5 dB reduced sensitivity at both 90/270 degrees and 180 degrees off -axis, walks the line between these aspects. See their explanation here-
https://www.bblist.co.uk/pdf/sennheiser/supercard.pdf