PvE? You won't need either of them. Perhaps Ominous Flame can be used for Darkmoon trainer Tonk.
PvP. Well, outside of people trolling with Fade Before the cooldown was applied I don't think I have ever faced either of these two pets. Very very rarely if I have.
Ominous Flame got the Conflagrate combination but that is not all that powerful. Jadefire Spirit seems more defensive with shield and heal/fade. I think you can get slightly more team-use out of the Ominous Flame since it has the Curse.
Both pets, however, are quite nice bird killers and will both do well when you keep running into triple darkness birds for example. The Ominous Flame might have one-up here since it can change the weather to help your teammates. I am actually not sure if the healing from the Jadefire Spirit is affected by the Darkness, if not it might be worth looking into.
Not sure I was helpful at all.