Celebrim
Legend
So would it be fair to say that you don't believe divine magic would be able to compete?
I think this entirely depends on several things:
1) How universal is the hatred and fear of magic? Can society at all levels be trusted to turn against a spell-user, or our there subcultures within the society where you are either tentatively accepted or at least tolerated? That is, do criminals also cry, 'witch' and turn you over to the mob? Are witches or wizards tolerated in rural areas as a resource of magical aid long as nothing bad can be blamed on them? Are the educated or ruling classes more likely to be fanatical in this cause, or to pay it lip service while retaining magic users for thier own purposes? If there are subcultures that the spellusers can find refuge in, its far less of a problem than if literally everyone is unquestioning of the assumption that magic is universally abominable.
2) How powerful politically are divine spellcasters? Is testimony about the results of a spell admisable in court, and if it is, is that considered any more definitive of testimony than any other eye witness account? This is a very different circumstance than any priest which casts 'Detect Magic' being able to cry 'Warlock' and arranging an execution on the spot.
3) How powerful do you plan legitimate spellcasters to be mechanically? Say there is a rural village of 300 people, the highest level priest serving this community is probably - 1st, 3rd, 5th, or 9th level? By extension, what is probably the highest level priest in a nation or region. (In full disclosure, I would probably answer those questions as 3rd and 8th respectively)
4) It's less a questions of whether divine magic can compete than how much the society loses by not having both divine and arcane spellcasters to protect itself with. But in general, divine magic can't compete. There are somethings it can do well, but arcane magic can and does do just about anything. It is generally more poweful, that's why divine casters can wear armor and get more hit points and better BAB progresssion to compensate. In particular, the usual low level suspects - charm person, invisibility, web, fly, fireball, etc. - are a big deal if you can't respond in kind or at least set up arcane defences.