I'm in the market for a polarizer and have 2 I'm looking at - both
near the same price.
1) Hoya Pro1 Circ Pol (58mm)
2) B+W 58ES SLIM CIRCULAR POLARIZER
Hoya is multi-coated, and I'm guessing the B+W is not (but probably
has some sort of coating??).
I have a B+W slim Kaesemann polarizer and it's a huge PITA. It ships with a shallow Schneider plastic cap that you're supposed to use because they're too slim to use a proper lens cap. The plastic cap falls off constantly. It pretty much won't stay on the camera unless the camera is sitting on a table with the lens facing the ceiling. Even then a strong breeze may foil you.
Would I be better off choosing one of these over the other - with
image quality in mind?
Both the Hoya and the B+W are good polarizers. I prefer the B+W MRC coating and the Hoya Super HMC coating to the coatings on either of the polarizers you mention, but neither of them is a bad product, IMO.
When you use a filter you're making a trade-off. You're risking a loss of contrast and a greater likelihood of flare in exchange for protecting the front element of your lens and providing whatever effect the filter provides (in this case polarization). The better the multicoating the better your chances of avoiding optical artifacts from that extra sheet of glass.