Well, there is no general "policy". Jeff once said:
In general there should be one answer per person per question; if you need to amplify your answer, edit it!
The reasons why I think there should be one comprehensive answer on Super User:
The question asks for a solution to one problem, so your answer should contain everything the user needs. You can always logically split up one answer into multiple parts, using horizontal lines and headlines.
Posting multiple answers was useful when we had poll questions, e.g. "What is the best XY to do this and that?", "What was your best moment in a programmer's life?". This would allow people to individually vote on suggestions based on their personal preference or opinion. These kinds of questions are not really acceptable anymore. If a question has an unlimited set of answers, and every answer would be equally valid, it should probably be closed.
Voting should primarily be based on the usefulness of your answer. Your two answers were probably equally useful and very much alike, I don't see why they should be completely separate. I don't think there would have been upvotes on an individual solution, and I also don't think there would have been any individual downvote.
Posting multiple answers could make sense when you have two very different solutions likely leading to diverging vote behavior (e.g. a full, complete solution vs. a workaround).
Discussion about a solution should belong in the comments anyway and result in an edit explaining further details if needed.
If both answers work, only one can be accepted.
And finally:
You're essentially gaming the system. By posting two answers that could also stand as one, you're getting double the reputation. I absolutely don't mind you getting reputation (I even upvoted your answer), but there should be no reason for users to gain twice as much as others do just because they posted another answer.
I've never really seen people answering a question twice on Super User. It really deviates from what we usually do.
There are certain cases where users post a non-working solution and instead of editing it to correct it, they post another one, and yet another one. This occasionally happens and shouldn't be encouraged.
Note: This is rather focused on the topics of Super User. As I said before, poll-types of questions rather encourage posting multiple individual answers, but they are not allowed here.