In most cases, Skill Based MMO games belong to the MMOFPS or MMORTS genres. Those games are less casual and straightforward than others, so the developers have an opportunity to create an ultimate competition challenge. It also happens because games of this genre will not succeed if they are not based on the player's ability to play. No one will play a shooter where shots fly past the enemy because its level is higher than your character's.
In MMO Skill Based games, the system of character development is usually based on blocks of various skills offered to the player. Such games also typically do not have specific classes, or they have a wide developmental variability.
PvP in Skill Based games is one of the main features of this genre. From simple battles where you only need to press the keys in time and know the tactics of the fight against other classes, in Skill Based MMOs, you can rely entirely on your PvP skills. You can only guess about the tactics of the opponent by its actions. You can't just crush another character by pressing all the buttons of skills in a row: you need to understand when the enemy is open to strike; you should know when you need to use the skills. Such knowledge and abilities are acquired only with the game experience, which takes a lot of time. Therefore Skill Based MMOs are not very popular among casual players.
ArcheAge is a Skill Based MMO without a strict vector of character development. There are 12 skillsets, and you can combine them as you want. It makes PvP part of this game dynamic and unusual.
Blade and Soul has a complicated skill-based combat system. This game is all about your tactic and battle wisdom. You should see the enemy's weak points and use your skills just in time; otherwise, you wouldn't be able even to enter the PvP arena.
Albion Online has a unique skill system, which manifests itself in PvP and GvG battles. It's both complicated and interesting because abilities in this game are levelling up only if you use them often, so already to the middle levels you will begin to become a master of your skill.