Let's just go with this:
If your definition of character is as strict as the exact representation of the character as it was before, then I'll concede that they are not the same characters. However if you can ever consider that a role can ever be symbolic in nature, then you should realize how much these two examples have in common.
When a director says "This is a David vs. Goliath" story, you don't just say "that's not David" and be done with it. That's not all there is to it. There can be many layers to add to it to make the characters stand out from their inspirational sources, and that's great, I would consider those two to be both the same character and different characters at the same time, depending on the circumstances of the conversation.
However if you're going to give me: The same plot; nearly the same setting; a "remake" or retelling or however you want to label it (it's not a sequel and starts from the beginning, where the original started off at), give me very similar characters that fill the same roles as the original source, and then tell me that those characters are not the old characters that they're based off of... I'm sorry but I just can't agree.
It's like one of those knock off Disney movies of ages past, where all the characters had different names and the animation sucked, but all of the events followed basically the same exact pattern and/or theme. (as far as I'm aware these things are still made)