There is also a difference in the quality or scope of answers.
I've seen some questions that have had an answer of only a couple of sentences. While I've agreed with those sentences, I've felt that the same thing could have been said more effectively with more discourse, references to external sources, and so on.
In these cases, the quantity and quality of things that I'd like to add to an existing answer are ineffectively relayed in a few comments. As such, I've posted my own answer. Most of the time, mine end up being quite more detailed than the original answer.
On the other hand, if I'm mostly satisfied with an answer but think it could benefit from an additional point, I comment on the answer suggesting that the author add that point. There is no benefit to duplicating something simply to add one or two lines to it.
The real question is, will your answer add significant value to what's already there. If it won't, then don't post anything. But if you think it will, then it makes sense to add your own answer.
(I believe the other answers here sufficiently address the issue of near-duplicate answers. I wanted to give this answer in order to provide a slightly different viewpoint.)
As for something being rewarded or punished, the voting should generally take care of that.