Omnidirectional mics pick up sound in all directional fairly equally, so when they are used in this manner, they pick up sound very much like the human ear does. Cardioid microphones are Uni-directional microphones and pick up sound mostly in the direction you point them. They cannot be used to make binaural recordings, but can, of course, be used to make stereo recordings. Because of this directionality, they have certain advantages over Omni-directional mics in some situations. I like to listen to my recordings with speakers, not headphones.
Binaural recordings sound best when listened to through headphones.
You can use Binaural or Cardioid mics to make stereo recordings. When you are recording in a venue that has good acoustics, the audience is fairly quiet and you are fairly close to the sound source, Omni-directional mics are capable of make excellent recordings and would be the mic of choice. In addition, when you specifically need to use a very small microphone, omni's are the better choice. Good quality Cardiods are about 2 or more times the size of equivalent sounding omnidirectional mics. The Cardioid mics that are commonly available in the same size package as the small omni's are lacking in deep bass and high frequency response.