Is deleting it and creating a new question ever a good alternative?
No, you should not be doing this. Whenever possible, fix the question up rather than deleting and recreating. If you've asked a bad question and it hasn't yet been answered, then by all means, feel free to self-delete it. But don't reask it exactly how it was before.
If it is, when should I choose which alternative and why?
As I said previously, you should not delete and reask your questions. You should instead be editing them into shape so they are good, on-topic questions. However, you should not completely change the meaning of your question through edits.
Is down votes on current question something that can be considered?
Downvotes simply indicate the number of users who though your question was badly-researched or otherwise not useful. Do not delete your question because it was downvoted. Edit it. Edits bump the question to the homepage where it can be upvoted and downvotes can be retracted if the downvoters view the question again. Also, if the question was closed, edits relatively soon after the question was closed (I'm not sure of the exact numbers) push the question into Reopen Votes where users can vote to reopen or leave closed.
If the question's simply not a good fit for the site and can't be edited to become on-topic without completely changing the meaning, then that's okay. Sometimes edits just aren't enough to fix something without changing the whole meaning (which, by the way, you should not do through edits). Learn why it was off-topic and avoid asking things like it in the future.
Assuming the question is unanswered, what would be bad with creating a new instead of editing?
There's nothing wrong with this, as long as you ask a different question. As mentioned before, you should not self-delete and repost the exact same question. If you wish to self-delete while the question's unanswered and you want to ask something different, that's fine.
I would also encourage you to not self-delete if there's nothing wrong with your current question. Even if no answers were posted yet, there could certainly be one or more users in the process of writing an answer to the question. It's really frustrating when a question is self-deleted for no good reason while you're answering it, and also a little unfair to the author of the not-yet-posted answer.