There are certain things which seem to be near-iron rules in pop, and one of them is that cover versions that are the most effective have to have the right arrangements and sentiment, but more than that they have to have the appropriate singer(s) or there isn't much point to them. They end up being, even if everyone is trying really hard, giving their best, a bit awkward and perhaps dubious, as if someone is trying to pull a fast one over on the public.
Black's got a fine voice for a lot of songs but here she seems out of place, as if she is singing the song as close to its US version while remaining sturdily British in her noble sentiment. George Martin wanted to do something different with this, but it is not, ironically, different enough to really matter in any way. The Righteous Brothers did not get their name by holding back emotionally - the agonized high "PLE-EE-AASE" in their version is unthinkable here, maybe because Martin felt it unsuitable for Black to let loose; I don't know.
The near-apocalyptic storm of the original is something that should be approached (if it is to be covered) in an oblique way; this sounds as if Martin & Co. were far too close to it to be able to hear it any other way. There are many great covers of songs but for some reason this one comes to mind as taking a well-known original and making it new, as Ezra Pound would say, and giving the song a new life as well. In the end, Black's version was trumped by the original, as 1965, that snake of a year, slowly but surely began to change what was (the early 60s) into what was going to come, which at this point is still unthinkable...for now.