I went to Meta Stack Exchange (the Meta for the whole SE network) and dug up a question that linked to a Help Center article about your specific topic. If you just want the official policy, read the help center. If you want the community's broader take overall on plagiarism, look at the Meta question, or search https://meta.stackexchange.com for "plagiarism" for other related questions.
My understanding is that Super User's take on plagiarism is exactly the same as the network-wide or Stack Overflow policy. Indeed, here's the same page on the Super User Help Center.
Plagiarism - posting the work of others with no indication that it is not your own - is frowned on by our community, and may result in your answer being down-voted or deleted.
If there is strong evidence in the edit history of both answers of his or her content being modified to match yours with significant quotation or paraphrasing, that is plagiarism.
On the other hand, if your answer simply inspired the other user to change their mind and improve their own answer (without meaningfully plagiarizing you), that's probably acceptable.
Getting the right idea from someone else, and then doing your own research and putting in an answer in your own words isn't plagarism. If your answer is more comprehensive and useful in the long term, it will tend to get more upvotes.
On the other hand, if the other user put more effort into his answer and it looks more complete and well-written, they deserve the reputation they get from it.
One of the long enduring problems on the Stack Exchange network is the Fastest Gun in the West Problem, where often the first person to provide a (correct) answer gets the most upvotes, even if their answer is terse, lean on explanation, or mostly quotes external sources verbatim.
A valid response to the FGITW problem is to garner more upvotes/bounties by taking a conceptually correct but terse answer and re-writing it to have better exposition, more background explanation to set up the reader's understanding, or working out the solution in greater detail or with better pictures or formatting.
If that's all they did, then it's fair game.
If there's enough of your ideas in his post to be plagiarism, it's at least worthy of the community's downvotes, if not deletion.