Of the dozen or so times when a top ranked female tennis player played either a much lower ranked or handicapped male player, I think the male lost only once (1973 King vs Riggs, through there are claims that Riggs threw the match).
There exist sports where having XX chromosome is not a disadvantage. Male and female equestrians have been competing against each other in the Olympics since the modern Olympics began.
The issue of gender and 'what makes a woman a woman' in sports is not new. There are plenty of cases of men pretending to be women and claiming top prizes. I don't envy the officials who have to do gender tests , as there are many people who are neither XX or XY.
EDIT: now that I've had some time to go though my sources a little better, I should correct a couple things. According to the Wikipedia article, females have won more than a couple matches against males, though all of those matches involved either a handicap or a much lower ranked male. The Williams sisters themselves only claimed they could beat any male outside the top 200 (but they both lost by a wide margin in friendly sets to #203).
Male and Female equestrians have only been competing against each other since 1952, and not since the beginning of the modem Olympics.
I would love to try this, but I don't know how wifey would feel!