I think you are comparing apples to oranges, personally. The priest and beastmaster are vastly different mages with very different play styles.
To start with, I could not really say whether pet or holy avenger is better, because they do such wildly different things. Pet is about increasing your creatures damage and survivability, making it a force to be reckoned with. Holy avenger is about creating a distraction and providing some board control. The avenger protects your mage and gives your opponent a catch 22, while the pet simply creates a bigger threat.
You can compare malakais fire to battle skill, in which case the latter is a free constant +1 damage, and the former is an optional +3 damage. Battle skill is cheaper and more reliable, but the fire is more powerful. Different people will have different preferences whether they prefer reliability or power.
The creature pool I agree is a legitimate complaint. Disregarding going out of school, the beastmaster has a lot more options at his disposal.
As far as being mana starved goes, I kinda feel like every mage is mana starved when I play, lol. No matter which one I play, I always want to do more than I can. I don't really see how this is worse for the priest. 9 channeling is the same as the beastmaster and other aggressive mages. You say he only has 8 because of malakais fire, but you are forgetting that that ability is optional. You do usually want to use it, because there are few things I would consider to be better than 3 damage for 1 mana, but it is still a choice.