Well, it's a bit more complicated because when a male transitions to female there is a lot more involved than just a few odd surgeries. Basically every transwoman starts with a pill cocktail that stops all production of testosterone and replaces it with estrogen. The person experiences a decrease in muscle mass, because the Testosterone isn't strengthening it up anymore. their fat gets redistributed to the hips, butt and breasts. the final result after 5-10 years of estrogen is a body almost identical to a female body. Transwomen have less muscle mass than men and have a bit more of weaker bones, but not terribly weak, just female level of weak. If a transwoman has had the bottom surgery, then no testosterone will ever be produced in that body ever again... no testicles does that, but estrogen has to be taken via pills or shots because ovaries can not be created in a human body... just yet.

The only advantage a transwoman might have would be a bigger bone structure. But then, that's only a real advantage if you've got the male muscles to power it.

As far as the science is concerned she is as real a woman as any other woman on the planet. All fetuses start as a default female, so yes boys, you were once girls, which is why men have nipples, because they're left over from the female times in the womb. To become a male the fetus gets a hormone bath from the mother which changes the external genitals from vagina to penis, and yes, your penis is just a giant clit. But the first hormone bath only changes the external genitals. A second hormone bath is required to change the fetus brain into a male brain. For transgender women, that second hormone bath never happened and they end up being born females with male genitals, because their brains never got changed from female to male. Most transwomen end up hiding their feelings that something isn't right until they're past 18. They pretend to act like boys and most people never know that they have a female brain. Since they hide for so long they have to endure the male puberty and end up looking just like any other guy out there. But many of them eventually realize they should never have had the male genitals and they seek out treatment to make their bodies match their brains. That process of matching body to brain is called transition, which involves cutting of any further testosterone production and replacing it with estrogen. They basically have a second puberty of growing breasts, wider hips and decrease of body hair. Their muscle mass significantly decreases without testosterone and by the time the transition period is over their bodies are almost identical to any naturally born female.

But from what I understand is that Fallon Fox is still pretty early in transition, so her muscle mass might still be a bit high for a female. Actually, based on what I read on wiki, it only says she's had the surgeries, nothing about hormones... which if that's the case, she's effectively a male. But I think its pretty unlikely for anyone to be able to get the surgeries without already being on hormones. So my best guess is that she is on hormones, but it might be a bit early for her and she still has some extra muscle mass that gives her an advantage.

One would think there are doctors monitoring her to see if her capabilities are more in line with a male or female and then the promotion deciding where she can fight based on the doctor's reports. Also wikipedia says she is closely monitored by Olympic Athlete standards for transwomen.

I think its best left to the people who allow her to fight whether she fights with the men or women.