I think tennis, because of the existence of mixed doubles, is probably the only sport that has even dared to dabble in men vs women, even as an exhibition contest.
Let's see how these matches have gone recently...
2003: Yannick Noah vs. Justine Henin
In December 2003, Yannick Noah and Justine Henin played a friendly match at the Forest National in Brussels. Noah donned a dress for much of the match. He played predominantly trick shots and slices, but still ended up winning 4–6, 6–4, 7–6.
2013: Novak Djokovic vs. Li Na
In October 2013, Novak Djokovic and Li Na played a light-hearted exhibition mini set in Beijing, China to commemorate the tenth anniversary of the China Open. Djokovic clowned to the amusement of the crowd, and at one point swapped places with a ballboy. Li was given a 30–0 advantage at the start of each service game, and she went on to win 3–2.
Let's drop this stupid idea that women can compete with men in professional sports...and for that matter, let's get some real fucking science on trans athletes and their competitive advantage (or lack thereof).