Someone in this thread wrote to me privately and asked for my comment. So this isn't a direct reply to anything that's already been posted; it's more like, if you take a step back and ask about cardioid vs. supercardioid, what are the issues?
The thing is, stereo recording goes beyond the behavior of the individual microphones, and gets into how they work together. In that respect, if I were forced to give up one pattern completely, I would sooner give up cardioids than supercardioids.
(a) Most microphones that their manufacturers call either "supercardioid" or "hypercardioid" are neither; they're nearly always something in between those two patterns, with their specific parameters chosen for whatever applications the microphone will be marketed for. Most directional microphones are designed for communications, since that market is many times larger than the market for music recording. When a manufacturer uses the term "hypercardioid" it tends to imply that the microphone was designed for speech pickup, and will sound thin when used for music recording. The exceptions can be counted on the fingers of one hand and you wouldn't even need to use your thumb.
(b) Cardioid is a rather broad pickup pattern. Whoever thought of calling it "unidirectional" owes the world an apology. Cardioids have barely enough directivity to be usable for coincident stereo recording--and when they are used that way, they generally pick up too much from the center; the result is often halfway to being mono, particularly at low frequencies (and particularly if the cardioid is dual-diaphragm, for reasons I won't go into here).
At the side of a cardioid, the response is only 6 dB down from the front. If someone is being loud and obnoxious at 90 degrees from you, they'll still be loud and obnoxious in your cardioid mikes--and since those mikes are almost certainly angled apart to some extent, the disturbing sound will probably be nearly on-axis for one of your mikes. Supercardioids let you get equivalent spaciousness with less of an angle between the capsules (or choose whatever compromise you like).
(c) Supercardioid isn't a very narrow pattern, either, but it's definitely different enough to "earn its keep". And the difference gets multiplied several-fold in stereo--partly because of how our ears and brains work, and partly because the difference is in three dimensions rather than only two. Supercardioids used for stereo recording have much less of the "too strong center" problem, since at any given moment on average, the two channels have more difference between them than you would get with cardioids placed the same way. There's more "mutual exclusivity" between channels for any given angle and distance between them.
(d part 1) All other things being equal, a supercardioid of a given type of construction will generally have a little less low-frequency response overall than a cardioid of similar construction. But it's at least equally important (1) whether the pattern is maintained at low frequencies or "blooms out", and (2) how the microphone responds to standing waves in an enclosed space (which is mainly a concern at mid-low and low frequencies). For the most part a supercardioid (again, "all other things being equal") will keep its pattern better at the lowest frequencies AND will be less influenced by standing waves. Both attributes tend to make the low frequencies sound clearer on a recording.
(d part 2) Paradoxically perhaps, a stereo recording made with supercardioids can often feel more spacious than one made with similarly-placed cardioids, provided that the capsules are angled apart far enough. That may go against some people's expectations, since they reason that a narrower pattern -> less overall pickup of ambient sound. But what our ears and brains respond to is "difference-between-the-channels" information, especially at low frequencies--and cardioids (especially dual-diaphragm cardioids, i.e. all electrically switchable types) are rather bad at delivering that information, while supercardioids are generally better at it.
--best regards