Difficult to answer, really, because in Britain, both these plants are only annuals or biennials, not something that keeps going and spreads for miles. Hopefully someone else in a hotter region might see your question and be able to answer.

I'm pretty sure that echium vulgare is an annual by habit and unlikely to be perennial even in warm areas. It does self-seed very easily so that is likely to be the worst problem. But it's such a pretty plant, why would you care?

If it is anything like the echium fastuosum, the volunteers will keep you busy. My area is like San Francisco, and if I prune my echium f. when the flowering stops, it has lasted for five years. But the seeds sprout freely in the fall.