Intriguing. What's the main difference with regards to puristic recordings with two mics - omni or cardioid or whatever - which are spaced?
They are not spaced!
Sorry couldn't resist.
You can do single point recordings with two ribbons. In this case one stereo mic simply makes alignment and everything else simpler. You can do single point recordings with two cardioids or any of the others. The differences are mainly two things. A pair of figure 8s have identical (though reversed) stereo pickup on the front and the back. So you can spread musicians around better on two sides instead of simply in front of a pair of mics. Figure 8s also pick up more of the room sound or the sound of space than other single point stereo miking techniques. That is good if the space is okay. Maybe detrimental if the space is poor. When it works you get a better cushion of air around the sound of the instruments.
Another potential advantage that usually isn't fully obtained, is crossed 8s can reproduce the captured sound field more accurately than other techniques. This fully true only if your playback speakers are at a 90 degree angle from the listening position. Usually few people have speakers more than 60 degrees apart.
Whenever mics are spaced apart you de-correlate the two channels which causes noise to add artificial spaciousness. That can sound fine, but it isn't an accurate rendition of the space. This is true of cardioids or omnis. You also can get comb filtering effects that sometimes aren't objectionable, but aren't high fidelity to the original music. If you read the patents on stereo by Alan Blumlein you find that single point miking works for stereo as the playback effectively adds delay equivalent to the width of your head between channels (sort of like dummy head recordings over headphones). If you space mics apart you can alter the proper effective spacing and muck up the real stereo soundfield.
Finally, a purely blind subjective opinion. I have listened to at least a dozen online comparisons where a performance was recorded with multiple techniques using only two mics, and you were given the files to listen to and rank. You didn't know which technique was which until you made your choices. I always have chosen for enjoyment, natural sound and simply what seems the best quality those that were done with single point mic pairs. Normally a mid-side or blumlein I rank the highest. Single point cards are usually next. Spaced techniques vary more. A well done spaced pair of omnis can be very beguiling itself.
Now when I have recorded both ways you sometimes do a test and the false space of spaced pairs seems the way to go. Quite often people will use a single point pair as the main mikes and flank them with spaced omnis. The omnis give excellent bass and some space. This is blended in whatever amounts seem appropriate (often one third or so). So your imaging is anchored with the single point pair and some ambiance and low end come from the spaced omnis. Yet at the highest levels over a very good playback rig, the one pair in one point of space seems to work the very best.
A quick comment on ribbons. They just have this sound. It varies and some of the niceties seem common to most of them. They are quick and clean and smooth and musical. You can hear the deficiencies in frequency response and yet they seem to transcend that. Now something like the fine AEA R88's don't have much in the way of those deficiencies. One can also use bidirectional condenser mics in much the same way. Yet they don't quite sound the same. They sound excellent, yet different. One is a velocity gradient mic and the other is a pressure gradient mic. Something J_J can tell us more about if he will.
So these are some of the legion of reasons that Watchnerd mentioned.