Closing a question as a duplicate explicitly does not delete a question, nor does it put in on "the path to deletion" as other close reasons do, as such the existing good answers are not lost.
The purpose of closing as duplicate is 2-fold;
- Pointing to a single question where (hopefully) the best answers can be found.
- Preventing good answers to the same question being spread across many locations.
A question already having answers is not against either of these goals, it is certainly unfortunate that it was not closed sooner, but that is secondary; new answers to the secondary question are still a bad thing, if they add something new they should be added to the primary question.
If both questions have particularly good answers then flag to merge, but either way it is good to close as duplicate to prevent further answers being given to the secondary question.
Equally if the old question has low quality answers and the new question has good answers then vote to close the old question as a duplicate of the new question; time of posting isn't important, only the quality of the answers.
Questions that are slightly different
If the questions are sufficiently different that an answer to one would not answer the other then you are correct to leave them both open (a comment to note the existence of the other for more information is always useful however)
Good duplicates are helpful
I will often upvote questions that are already closed as duplicates if they are well written and will provide useful "ways in" to the main question for search engine; treat upvotes not as evidence against closure as a duplicate but simply as a sign that it is a quality duplicate