The "zoom" in zoom climb refers to the ballistic nature of this climb, as opposed to a steady climb. This means that most of this climb is from pointing your forward speed upwards and flying like a stone with a lot of initial speed. Prop thust helps some.
In a pure zoom, the plane would be at near 0 G. In these conditions, the difference between planes (starting from the same speed) will be rather small: 100-300 feet for typical combat speeds. The bigger difference is how planes handle at the top - some can really hang in there almost hovering, while others touch the top and immediately fall back.
In practice, zoom climbs are almost never pure zooms. They are a combination of a zoom climb and a regular aerodynamic climb using wings lift (hence not zero G). So when starting from speeds well above the typical climbing speeds of 150-180 mph, fighters tend to behave similarly. Then when speeds drop to the above range, the planes with the better climb rates start to gain. Spit 16, Zeke, La7 and Yak3 for example have very very steep climb angles (determind by the ROC/TAS ratio). This is not just their best climb rate - it's the climb rate at very low speeds. To rope them in a heavy poor climbing plane, the zoom needs to be near vertival to minimize the aerodynamic component and rely on the ballistic component.
So, to zoom climb away from your opponent, you'd better start at a higher speed than him, and dont expect to out zoom his bullets.