"Shotgun" is a type of microphone construction, not a pickup pattern. In the midrange and the lower end, shotguns are just ordinary directional microphones, often supercardioid-ish (manufacturers often fail to distinguish accurately between super- and hypercardioid). Only in the high-frequency range does the pickup pattern of a shotgun mike get narrower, starting typically at 2 - 4 kHz depending on the interference tube's length.
But the interference tube principle is primitive and brute-force, so this narrowing occurs in a jagged, irregular way. Published polar diagrams generally have spot frequencies an octave apart, which barely begin to show the true extent of this irregularity. At any given off-axis angle of sound arrival, the high-frequency response of the microphone can be wildly different from, say, its response just 10° to 15° from that same angle. I'm talking response peaks and dips of 8 - 10 - 12 dB--and that distorted sound mixes in with your main pickup, and can never be separated back out again. The degree of this jaggedness is one of the big things that separates $3000 shotguns from $300 shotguns, but they all have some; it's inescapable, given how they work.
For this reason, when using a shotgun mike it is imperative that the desired program material be kept strictly on axis. It has to be close enough to the sound source, and pointed accurately enough, to keep any direct OR reflected program material within the "sweet spot" in front of the interference tube. Otherwise you get varying amounts and kinds of sound cancellation at high frequencies. Boom operators on film and video sets go to enormous effort and trouble to get this right. The interference tube damps the high frequencies of diffuse, environmental sound, but it can't increase the proportion of direct sound to reflected sound in a linear way. A shotgun mike is NOT suitable for use in a reverberant environment where reflections of the intended material will reach the sides, top, bottom and rear of the microphone to any appreciable extent.
All the formulas for figuring out a good geometry for a two-mike stereo pickup assume that the microphone's directional pattern is the same at all frequencies. And you can't set up a pair of microphones with one distance and angle for the low and mid frequencies, but a different distance and angle for the highs. For a pair of shotgun microphones, no one angle can possibly exist that would be right for the whole audio frequency range; whatever you choose will be wrong in an appreciable part of the range.
As a result, using a pair of shotgun microphones for stereo pickup in an enclosed space, where you're not pretty much right on top of the sound sources, is a fundamentally flawed approach. Your odds of getting a good-sounding recording would be much better if you used microphones with a more consistent directional pattern across the frequency range--even though the diffuse sound pickup at high frequencies would be greater that way.
Professional engineers can't always put mikes where we want, but even when we have to mike from farther away than we prefer, we don't generally make stereo recordings with a pair of shotgun microphones. We might put up some number of them, say, to cover specific parts of a theater stage--but that's spot miking; it's not the main/master stereo pair. The signals from those spot mikes are mixed in to some appropriate overall stereo pair on an "as needed" basis. As an alternative, please consider what DigiGal posted a few messages up from here--she knows whereof she speaks. If you have a shotgun mike whose sound quality you like, pair it up with a good figure-8 for a mid-side stereo recording.
--best regards
P.S.: To answer a question that was asked earlier in the thread: There are many shotgun microphones, including expensive models from famous manufacturers, that sound different (especially at high frequencies) depending on how they're rotated along their long axis. For such microphones the manufacturer's logo or trade mark should be treated as a "this side up" indicator. John Willett is right in an abstract, Platonic sense that this "shouldn't" make a difference, but do check--listen to your own voice from off to the side as you roll the mike around, and you may well find that the rotational angle makes a considerable difference to the pickup quality.