The advantages of using a Z-Buffer versus prioritising pixels according to depth

Question

This is a bit more of an academic question. Indeed I am preparing for a an exam and I'm just trying to truly understand this concept.

Allow me to explain somewhat the context. The issue at hand is hiding objects (or more specifically polygons) behind each other when drawing to the screen. A calculation needs to be done to decide which one gets drawn last and therefore to the forefront.

In a lecture I was at the other day my professor stated that prioritising pixels in terms of their depth value was computationally inefficient. He then gave us a short explanation of Z-buffers and how they test depth values of pixels and compare them with the the depth values of pixels in a buffer. How is this any different then 'prioritising pixels in terms of their depth'.

Thanks!