On the height of the existing floor compared to surrounding floors, etc. If your hardwood floor is already at the same height or higher than floors in surrounding rooms, then you're going to have an even larger difference that might be really bad. If it's lower than surrounding rooms, you might be able to get away with it.
Personally, I'd have them removed unless you have a very good reason for leaving them.
And, out of curiosity, is there a reason you're having the existing replaced rather than just refinished?