Are any classes better equiped to quest?

The classes that can mob the best, or the class that has higher mobility. Depends on the quest. I know on certain quests that involved killing xxx amount of monsters, my NL (when it was an Assassin with high DEX) could still do it faster than the majority of the classes I was up against back then. Now since the times has changed, I'd say probably Cygnuses ANYTHING or just Arans, since Arans are fricken fast at hitting and mobbing.

Aran are also good at mobility, with Combat Step.