One of the amazing things about Cherenkov radiation is that it is not omnidirectional. There are processes (fluorescence, or scintillation, for example) which result in isotropic emission of light from materials. But Cherenkov light is emitted along a conical surface about the axis of the charged particle's direction of travel. As a sister comment said, muons tend to move linearly, so this light stacks up in a particular direction. Electrons, particularly at lower energy, scatter more, and that stacking gets washed out a bit.

That directionality is very useful. The directionality of a muon or electron produced from a neutrino interaction is correlated with the direction of the incident neutrino. That's interesting for the astrophysical kind of questions that IceCube is addressing, and it's also useful in other contexts (background rejection for fundamental physics searches, monitoring of nuclear reactors via neutrinos, ...).

Cherenkov radiation is indeed polarized, but to my knowledge that hasn't ever been made use of.

Tangentially: there's also some really cool work being done on detectors which utilize both Cherenkov and scintillation light at the same time, exploiting the directional (and other) differences to extract the most information possible out of each event.