It is much more the norm to race European and Asian female horses against males, especially on grass courses.
It ha been theorized that a female horse can compete more successfully against males on grass for a variety of reasons.
If you look at past results of foreign races there are many female winners of the great overseas races. The Arc de Triomphe, Melbourne and Japan cups among others. There are also several Breeders cup winners in the open races who were female.
If there is a comparable female race open the owners will generally take it unless they feel a victory over males will enhance the value or year end champion status for their filly or mare.
Of course there are generally very large gaps between the female winners of the American classics but very few actually try. If you compare the percentages of winers to starters, the females are probably winning at close to the same clip