Latex is the classic dipped coating: it grips dry, rough loads well and feels soft, but it is not the best choice where oil is constant. Nitrile handles oil and grease better and is the usual pick for workshops and oily handling.
PU is the thinnest of the three. It stays flexible and keeps finger feel, which is why it shows up in assembly and electronics work. The trade-off is less bulk protection than a thick latex palm.
No coating is waterproof on its own and none of them should be presented as cut-proof. Tell us the load, the oil level and the precision needed, and we will match the coating — and confirm the model at inquiry, not from a photo.