Here's my 2 cents:
If posting screenshots clarifies one answer over the other, and both are posted within the same time frame, then I'd see no problem with them being duplicates of each other in terms of content. Don't forget that many questions can be immediately answered by people who know what to do and why shouldn't they, after all? Also, questions that are easy to answer often result in only one possible answer.
If the duplicate answer was posted hours later, then however I wouldn't appreciate this myself if I was the first one to answer.
But: Don't forget that SE is also about the better answers getting more upvotes. If you can make an answer stand out by being more detailed, adding screenshots, clarifying things, then why should it not be here? If this answer happens to include the solution that is already there, but extends it and adds a significant amount of details, why not?
If I go through answers and there are two, one having answered the problem immediately but in a short manner, and one having clarified the steps even further, I'd probably give both of them votes.