Regarding the first gate, let me defer to details in Start of Darkness:

Spoiler
Show
You could say that was about power versus precision; or maybe brutality versus finesse. The defender was a wizard and the attacker a sorcerer, and Xykon demonstrated his theory of using one spell really well, versus a hundred varied tools.

Lirian's gate was about nature, which Xykon defeated by being unnatural. Or undeath versus life.

Either way, we don't really have much room for analyzing themes there, with so few character arcs.