The DA is basically as you put it, a furballing arena. It's
where people can hop on, shoot a few planes down real
quick, and not have to worry about score or bases, etc.
It's also -the- place for duels. It's somewhat private, has
all airframes/GVs available (for free), and is easy to have
a 'fair terms' fight with somebody.
The MA holds a little bit more purpose, and has conflict
between three countries on multiple fronts (as opposed
to a central 'DA lake'). Large GV battles, carrier action,
bombers, furballs... All found in one (or two) arena(s).