I would generally consider the following to tell me whether I should edit or post a new answer:
Am I totally changing the meaning and message of the answer, such that this new version has nothing in common with the old one?
If so, I'll delete the answer and make a new one. Otherwise, I'll edit.
The driving factor is the votes. Should the votes on the old version still apply to the new one? Are those peoples' votes still applying to roughly the same thing they might vote for? Editing an answer from "Yes" to "No" is probably something you shouldn't do.
People can reverse their votes on your answer post-edit, but the question is whether they'll ever find out and do so. The best rule of thumb might be to consider, honestly, how you'd feel if you were the voter and the answer was someone else's. Would you be fine with your vote still applying after that major change, or not?
Trivial examples of when I'll edit:
- Yes, because A B C. → Yes, because X Y Z.
- Probably, because X. → Yes definitely, because X Y.
- Horrible explanation of certain key ideas → Same key ideas, total rewrite of the explanation.
Trivial examples of when I'll delete my answer and post a new one:
- No, you can't do that. → Whoops, yes, you can totally do that.
- Do {thing that I realise is a bad idea} → Do {completely different thing}
I'm inclined to think your answer is in the "delete and post a new one" category, because it's a major message change and very close to a "no you can't" → "sure, you can" change.
Bear in mind you also have the option of keeping both answers. Consider: Is a Dragonwrought Kobold a True Dragon? - You might want to do this to allow voters to decide, or so as to not destroy still-reasonable hard work, etc. In this case, probably call out in your second answer why you're posting a second answer that contradicts your first, as KRyan did there.