Are they happy to give advice to others or do they keep useful hints and tips to themselves? The sprites in my Fairy Kingdom are upfront about loathing one another and fights are frequent. The higher magical species despise them for this but there is no love lost between the fairies and the witches, to name one example. It could be argued the sprites are at least more honest about their loathing for others.
Do the species in your fictional world interact with other species or do they limit inter-species contacts? Could there be a Romeo and Juliet situation set on your world? When different species do have to co-operate (maybe because they're all facing a fearsome external threat), do all the normal barriers come down or is there still restraint here? After the threat is dealt with, do the barriers go back up again or are inter-species relationships changed, for better or worse, afterwards?
For a book or story to be realistic, no matter how fantastic the setting, characters and species have to interact (so often this is the source of the conflicts driving the tale). It is how you handle this interaction that can ramp up the tension in your stories or kill it off completely.