This struggle with the concepts of how to be "competitive" without being "combative" is troublesome. I suspect we have gotten so used to using these words while meaning the same thing that we don't have a word for what it's like to be able to stop worrying about winning and losing.
What if we just "always try to do the best we can without worrying if we're 'better than someone else (or even how we were yesterday)' and just do the practice."
If we value the budo aspect of the practice then we must enter into the paradox of "caring whether we let the energy of the uke do its intended job or to get off the line, blend, take balance, and render that energy harmless" but not caring whether we "win or lose" or that we're "right or wrong" or that we're better than the other person. Just do the practice, try our best to survive a dangerous encounter (if it ever occurs), and let the relative dynamics of life determine all of those other things.