I'm no expert, but the main difference is that ambisonic mics basically capture sound at a single point, whereas binaural mics are positioned at the ears (so there's not only space but also a baffle). There is software that can create binaural sound from an ambisonic recording.
Another big difference is that an ambisonic mic gives you flexibility in manipulating the recording in post (for example, you can take a single ambisonic recording and, with software, convert it to Blumlein, XY cards, XY hypers, omni, etc), whereas that is not the case for binaural.