How would a non-poisonous snake compete? It will have fewer predator defenses, and hunting for its prey will be very different, possibly harder. Wouldn't the poisonous snake out-compete it, unless it ends up in a different niche?
Pythons and boas have been pretty successful. Realize that venom is not a silver bullet; have you ever noticed venomous animals very often pursue very small prey?
Venom has a place and a use, but just because you've got venom doesn't mean you're a superior predator. In fact, it seems to me it is most often used simply to allow a delicate animal to hunt prey that can hurt it- not because the prey is fearsome, but because the animal is vulnerable.
