Suppose someone asks a question. It has two solutions - one is easier than the other, but the other one has some benefits of its own.
For example, there was one question about imagemagick where the solution was either to re-build the package or to download and install the newer version from the website.
My question is which one is the better solution and also does the second answer need to be down-voted?
My question is which one is the better solution and also does the second answer need to be downvoted?
Not at all, no.
I save downvoting for things that are unhelpful, incorrect or just plain don't belong there as an answer. Just because it's another answer doesn't mean it's any less helpful to somebody else and it doesn't mean somebody else should lose reputation just because I prefer another answer.
This is your choice though.
Your example highlights the problem with some of the more technical answers we have here. It's not always entirely clear how helpful an answer is. If the answer is merely "Rebuild it from source", I'd probably -1 and be flagging it to turn it into a comment. If they stress the reasons why something so dramatic is useful and explain how to do it, that's a good answer.
Sometimes there isn't just one best answer. I'll often +1 several answers in a question because they all provide helpful alternatives.
