Classes only determine where a goddess is positioned and what it's going to do on the battlefield.

Tanks take lots of damage, warriors deal damage in melee, healers mend damaged goddesses, mages and rangers deal damage at range:

Elements however, are the more important bit. Fire counters Nature, Nature counters Water, Water counters Fire. Light counters and is countered by none:

The element and class of each goddess can be found in the Teams screen: