xorg is the latest iteration of a free implementation of the classic unix x window system, which has its own advantages and issues, but for the most part suffers bad code-bloat from tons of code designed to provide features that made sense in the 90s, and not today.

wayland is a fresh re-thinking of how a graphical system should work on modern unices (or at least linux, i don't want to start that debate now), but suffers from detractors because not everyone likes the way it implements things, and mostly because it isn't xorg and change is hard. (and also because not all software that people use work perfectly well with it)

source