Anytime I simultaneously strike men against a more advanced opponent my strike never connects. The best answers I've been able to get from asking more senior kendoists are: strike quicker; strike on top of the opponent; reach center sooner than the opponent.
These are all likely to be true to a certain extent but try as I may to improve each one of these I have never been able to produce a more consistent means of overcoming this problem.
The problem seems to be that when the two men-uchi's clash one's arms tend to push the opponent's arms out off center making it difficult for the off-center opponent to strike. So in essence, yes the person that is more centered sooner is the one who will win.
So I thought, what if, I am unable to arrive at center first (which is most of the time when I encounter advanced kendoists)? Am I always going to lose the strike?
So I tried the following: instead of attempting to strike men, strike directly at the lower part of the opponent's shinai near the tsuba in order to deflect it enough to clear a path to that will enable your shinai to reach their men. This is kind of like suriage waza except that usually when we do suriage we brush our shinai against the opponents on the upward swing. I've tried doing this for suriage-men but it's always been difficult because it takes up a lot of time to bring your shinai up and then down. This is especially problematic when the opponent is rushing in with a men strike at full speed. So what I am suggesting is a downward suriage. Ie. deflect the opponent's shinai on the downward strike just before it is supposed to connect with the men.
Yesterday I gave this idea a go. During waza exercises involving simultaneous men strikes, I tried with and without this downward suriage technique. I was quite surprised at how consistently it seemed to work. Against more advanced opponents I was able to strike their men as well as them striking mine. For less advanced opponents I was able to overcome their strike very consistently.