Early in the game:
All pets have comparable melee (fire melee damage is lower though)
-Earth has highest hp and casts a damage-less nuke
-Water has 2nd highest hp and casts a nuke ... paired with higher melee dps it will out dps the others
-Air has the 3rd highest hp and casts a damage-less stun ... no more or less dps than earth
-Fire has the lowest hp and the weakest damage output (no kick/bash) but casts a pretty good nuke on top of an overpowered self damage shield. Not tanking it's dps is worse than the water and maybe as good as air/earth (not sure if parsed). While tanking it will run circles in damage output over the other pets.
Early on?
Water will do the most dps in a group. It's a nice mix of dps and survivability
Earth is the tankiest
Air is meh unless you need stun ... and even then meh
Fire is not great for groups, it has low HP but is excellent for soloing
At high levels water gets backstab, air gets a nuke component to stun, earth tanks like a beast.
When in doubt, all the specifics can be found here:
http://wiki.project1999.com/Pet_Guide