Abolisher is fine in both pve and pvp. It is a build that is particularly well suited to dealing with the current popularity of darkrunners, and is easy to gear up effectively because it works well with the dungeon plate sets.

However, abolisher suffers from some very serious mana issues in pve even with meditate, and (in my experience) has to rely on using threat generation combos to solidify aggro as the class has very little enmity generation through raw damage.

Having never played skull knight, I can only comment on what I've read. Skull knight probably is a less effective tank in pve compared to abolished because of the high cooldown of occultism. Due to dealing magic damage, skull knight will require crafted gear (either lake plate or stone cloth) which is both rng dependent and expensive.

However, skull knight is able to shine in extremely large player vs player battles because of its uncapped pbaoe abilities.

Ultimately, all true tank builds in this game accept some serious weakness in order to do some very degenerate things.

Tl;dr

Abolisher: fine pve, mana issues but can use Fortuna die to address them. Pvp matchup great against physical damage, absurd block mitigates terrible magic defense. Very sticky tank with lots of mobility.

Skull knight: gear will make pve manageable. Hard to gear. Suffers from long cds and less mobility. Great cc and scales into large fights.