I have just seen this answer Password manager for Linux with just working in-browser autotype Using the tool myself I'm sure I could write a better answer (more detailed, with screenshot...).
So should I edit the one already there or should I add a new answer that says the same and more details?
It depends how far the answer is from being a good answer.
If the answer explains how 4 out of 5 requirements are met but doesn't discuss the fifth, edit it. If all you'd want to add to the answer is a screenshot, add one. These are minor defects, and we are encouraged to edit to “clarify the meaning of the post”, “include additional information only found in comments”, “correct minor mistakes”, “add related resources”, etc.
If the answer just says “use this product” without explaining why, this is not at all the kind of answers we want on the site. Flag it as “very low quality” and write a proper answer.
In between there's a range where it can be ok to post your answer even if the first answer is to stay on the site. An answer is defined not just by the product it recommends, but also in the way it recommends it.
In the case of “gnome-keyring is a good password manager that comes with Ubuntu”, I encourage you to post an answer about Gnome Keyring that matches the level of detail of the LastPass and KeePassX answers.
As for editing other people's posts - I believe edits should not deface, misinterpret or paraphrase entirely what has been mentioned by another person. An edit makes sense when the answer has broken links, horrible grammar, formatting problems and other reasons that may prevent the readers to better understand and apply it. Usually the review system of the Stack Exchange sites allows for reviewers to flag invalid, too minor or destructive edits appropriately.
That being said, your edit might have all the good intentions, but it could never make it live due to the review system itself. Apart from that, the author of the post might disagree with your suggestion and your edit could become a reason for frustration, and series of comments like "hey, I never had the intention of posting this, revert it please".
A new answer will avoid the above issues. I'd personally write my own answer, in case it will significantly differ from the existing one in the following cases:
In other words, if the answer can be of value to he OP or users with similar problems, then it is good for the community to share your experience and expertise. If the answer is not that good, the community will react accordingly anyway, so obviously this is a good-enough criteria if you doubt whether "to answer or not to answer" - if it will be good for the community then do answer :)
In cases where the answer is close to yours, and the differences or improvements are insignificant enough not to write a separate answer, you could address your concerns as comments. If the author does not reflect them, they will still be available as a comment, and as such will add to the answer.
You should give the original answerer a chance at writing a better answer (seems like that has already been done). If they don't, and you think you can make a better one, by all means do so.
I don't think you should edit their post, since:
A: They didn't do any work towards a good answer.
B: It won't have a proper score, since the votes it has already are for the old, bad answer.
