I'm sure this differs from school to school, but I would assume they have all of your information still on file and will most likely use last year's letters in addition to whatever you submit this year unless they state otherwise.
It definitely wouldn't hurt to get another recommendation, perhaps that was one of the items that wasn't strong in your past application. Another letter would certainly help.
Along with that - you don't really know what your recommender said unless they provided you with the letter. Perhaps it was generic, or what they had to say about you wasn't exactly what HBS was looking for. It might be better to receive a recommendation from a new source. As you said - different perspectives. I think that this would be the way I would go.
"You may not realize it when it happens, but a kick in the teeth may be the best thing in the world for you." - Walt Disney