I tested with my friends and found the bonus .
red dragon pet gives +5 mana regen, +10dmg and + 1armor
blue dragon pet gives + 1mana regen, +10dmg and +5armor.
but i think that these bonus are bugs. because Dev said that we can get SET bonus when we wear dragon armor, helm and pet.
now,we can get the bonus from dragon pets(red and blue) without others(helm and armor).
I don't know about full set(dragon pet with armor and helm) give which bonus.