Comparison: It's plainly obvious when comparing these three that one class is vastly different. The Bear Shaman does not play very much like a caster at all -- you put on your 1 hour buffs, and then the only casting you'll really do ffxi gil is to use your HoT's before a fight.
From there it's mostly melee combos with the occasional heal, and thus, the BS is far removed in play-style from the other two priests.
The Priest of Mitra and Tempest of Set feel like pure casters. People wanting that play experience and to play a priest will be tossing up between these two.
So what makes the PoM seem to have better survivability early on, even with the ToS' powerful Lightning Strike? For one thing, while they each have an hp buff, the PoM's gives about twice as much hp at the same level -- but they don't end up too far apart in terms of total hp.
Part of the PoM's advantage could be the Repulse spell, which is extremely damaging, and the knockback gives a chance to get off a few spells without taking hits.
Having said this, the Tempest is perfectly capable of surviving these lower levels, it may just take a bit more ingenuity.