TheIf the answerer's being the author of the software adds additional value to the answer, then the second one - it's the most authoritative, and thus usually the most useful answer.
If the second answer comes in later, don't even be afraid of switching accepted answers. It will sting the first answerer a bit (especially if they've put a lot of research into it - I've been in that situation, too) but it's the right thing to do.