I think you're being a little silly :-) I think you should look at it as a super fun thing, with a little competition and both should be happy for the one that places higher. Don't look at it as losing, just a fun time and maybe next time the rolls will be reversed. We have a couple in our club that both compete, they really don't even think twice about it. They cheer each other on, it's great.
My SO doesn't work dogs, but we've competed in other things and we have a blast...ragging on each other, helping each other, and in the end being happy for each other. You can't avoid it forever in this sport or life, mine as well get used to it ;-).