There were numerous differences, but they most chiefly boil down to the fact that Legions were made up of citizens and auxilia were formed from non-citizens who would usually be rewarded with citizenship after they served one full term of service (between 20 and 16 years depending on the era). Legionnaires were always higher paid, I believe as high as 2:1.

Because of the diversity of the peoples who were considered non-citizens (especially compared to the rigid uniformity of the Roman legions), auxilia were far more varied. Batavian auxiliaries, for example, were well-regarded for their ability to swim while on horseback, and so were used principally as fast, powerful marines.