Dub,
It's just a question of the number of speakers that the recording is intended -- recorded & mixed -- to support.
A 5.1 surround recording is made for two front speakers, two rear speakers, one center-channel speaker, and a sub-woofer -- as shown below:
Usually, in 5.1 set ups, the rear speakers are smaller than the front speakers, and the center-channel speaker is purpose-built specifically to support movie dialogue. (There are purely musical recordings that use 5.1 surround. But I think the format really took off with the advent of home theaters and watching movies at home. OTOH, Quadraphonic was/is for music only.)
Quadraphonic recordings are intended for two front speaker and two rear speakers. Unlike 5.1 systems, (I think) most folks used the same four speakers for Quad set-ups. Back in the 1970s when Quad LPs were introduced, you needed to purchase an amplifier that supported Quad LPs plus two "extra" speakers. Most folks assume that those extra costs are what caused the format to fail. Others objected to the format because it's not necessarily an accurate portrayal of how we hear music in "real life"; it's as if you happen to be sitting among the people making the music. Sound is coming at you from every direction. If you want a "realistic" concert hall-type reproduction, then Quad is not for you. So music-audio purists disliked Quad, just like they (usually) dislike surround set-ups.
My assumption is that most listeners who buy a Quad recording today will be listening to them on their surround systems. If you've only got a two-speaker/traditional stereo set-up (like most music listeners, as opposed to movie watchers), then it wouldn't make any sense to buy a Quad recording.
Good point! Hadn't thought of that.