Just a general comment about microphones and recording distance: Yes, a diffuse-field omni (or something in that direction) helps you get a desirable frequency response for more distant recording, as compared with a free-field type. But getting the frequency response you want is just one issue, while the degree of reverberation vs. direct sound in the recording is another. Just because a certain type of omni gets you good frequency response with distant placement, doesn't mean that you'll like the result if it's all swimmy and swampy.
No one is saying that an omni mike is necessarily the best choice or even a halfway good choice for distant recording; it's just that IF it proves to be a good choice (given the sound sources and the nature of the space in a given situation), THEN a diffuse-field omni is the type you'd most likely want to use there (and I suggest add-on spheres as well--they really do help to overcome distance). But in many years of recording, I have experienced that situation only rather rarely. Now, normally I'm the hired engineer at the performance, so within the constraints of sight lines and lighting, I can usually place my mikes where I feel they need to be. If I'm forced to make a recording without that privilege, and instead have to place a pair of mikes farther away than I consider optimal, with no spot mikes of any kind, I would use supercardioids as 2manyrocks suggests.
However, any microphones used at a distance need to have off-axis response that is highly "listenable" (e.g. not peaky in the treble), since so much of the arriving sound energy will be arriving from off-axis. Among supercardioids that quality is available only from small, single-diaphragm condensers--and even among those, you still need to choose carefully, since most manufacturers of highly directional microphones (including both supercardioids and shotguns) are aiming for the speech pickup market primarily (film, video, PA sound, etc.) where intelligibility is the goal at the expense of naturalness. In a diffuse sound field many highly directional microphones--not just low-priced ones--tend to have rather weak bass response and a peaked-up upper midrange, followed by a steep drop at higher frequencies. For music recording you want microphones that are smooth and flat in their overall response, i.e. their off-axis response runs essentially parallel to their on-axis response, without excessive peaks or dips.
This is where polar diagrams will tell you crucial stuff that a frequency response curve alone can't. It would be even better if manufacturers would publish diffuse field response curves for their microphones--but unfortunately there is no standard method for producing a test signal for that, so the diffuse-field response has to be inferred from the 0-degree curve and the polar diagrams.
--best regards