Some Classes are better than Jobs when you're solo since they let you set more cross-class skills (double the amount that you can set on a job) and the classes that you can set skills from are far less restricted (Jobs can only set skills from two different classes, Classes can set from almost every other class).
Jobs get a raw stat bonus and their own special abilities that make it more suited to one particular role, making them infinitely better for party play (an exception that I know of is in the case of Paladin; there's almost no reason to use Gladiator once you've unlocked it since Sword Oath is pretty stupid).