With poetically similar language such as "destroyer of hope" and "bringer of hopelessness" or "taking hope" vs. "destroying hope", the semantics are typically not obvious. One needs to look at the surrounding context to determine what those phrases mean. However, there are general patterns which do occur in English speech that can be useful.
One key aspect is the concept of action. "Destroyer of hope" is an active phrasing which typically indicates an individual who seeks out hope and actively tries to destroy it. A "bringer of hopelessness" is more of a passive phrasing which typically indicates an individual who inspires hopelessness around them, but isn't necessarily actively trying to seek out hope to destroy. If anything, one might say that the cultivate hopelessness, and permit that hopelessness to counteract what hope it finds.
Again, this is not a 100% semantic rule, but it is a trend that I find tends to lead an author to choose one phrasing or the other. In the end, both may result in a loss of hope, but the way they cause that loss of hope is different and that is often conveyed by such phrasings. When facing a "destroyer of X," one might rationalize that it's a good idea to hide your X, so that the destroyer cannot find it. When facing a "bringer of not(X)," its usually encouraged to feed your X and make it shine brightly to overcome the miasma of not(X) that surrounds the bringer.
"Taking" vs. "destroying" on the other hand, has a more clearcut difference. Taking is an action that obeys conservation. If an individual takes X from you, you no longer have X and they now do have X. The concept of "taking back X" becomes meaningful to talk about. A destroyer does not try to conserve. If an individual destroys your X, you no longer have X and they also do not have X. There's no equivalent meaning of "destroying back X" which could be applied, although the idea of doing that starts to enter the realm of punitive measures as you find some equivalent of X that they have, perhaps X', so that you can say "you destroyed X, so I will destroy X' ".