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?
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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."