Connotation of "significant" or "considerable"

I know that they are interchangeable and mean nearly the same. But which of them has a stronger connotation in emphasizing the extent or importance more than the other? Or are they on the same level?

It depends on the context. In technical writing, we are very careful with our use of the word significant. We only use it when a number (some study result, for example) is statistically significant (with a certain p value, for example).

Even in nontechnical writing, though, I would say significant has a more technical, exact feel to it than considerable does. Considerable feels like a "guesstimate."