I recently realized that the quadras more or less correspond to the classic RPG adventuring party of warrior, rogue, wizard, and cleric. (To make the metaphor even more excessive, we could superimpose it over EyeSeeCold's fighting styles! )
Alpha - Rogue
: Rogues are notoriously curious and exploratory, and are rarely willing to leave an interesting prospect alone without checking it out. Rogues like to figure out how things work, and will usually start toying around with any clever traps or mysterious scrolls they find, regardless of whether doing so seems advisable.
: Rogues tend to present an easygoing, likeable persona, and value their own comfort and entertainment. They often see no problem with pretending or "stretching the truth" a bit. Rogues tend to act in a fairly relaxed fashion unless in danger.
Beta - Wizard
: Wizards are often very ambitious, and tend to place extreme importance on increasing their powers. This power is often attained via study and understanding, and a wizard will often leverage detailed knowledge about a situation in order to better control or influence it.
: Wizards can be highly introspective, and frequently like to plumb the depths of their minds or speculate on the underlying meaning of events. They can be quite theatrical and expressive, for example, a wizard might work himself up into a visible rage while casting a spell, while a cleric probably won't.
Gamma - Warrior
: One of the warrior's main jobs in the party is fighting off dangerous enemies in a direct, forceful way, and many warriors attach major importance to competition and conquest. At the same time, warriors tend to be fiercely loyal to their own allies, which they make slowly and keep forever.
: Warriors strongly value practical action over theoretical understanding. Intelligent warriors often their minds towards the tactical and strategic aspects of their trade, assessing the likely outcomes of battles and wisely backing out of those that could turn out poorly.
Delta - Cleric
:Clerics try to get along with everyone and support the other party members, although they can be somewhat uncompromising on particular personal principles.
: It's the cleric's job to keep everyone alive and healthy, and this is usually accomplished in a rather direct and diligent style. Whereas the wizard will occasionally pop in with major flashy effects, the cleric uses a more subdued set of protective and supportive abilities to good effect by constantly maintaining their effects and looking for where to best use them.