Round 1: Applejack vs. Amy Pond!
Applejack: Works on a farm with her sister, brother, and grandmother. When she was young she abandoned the farm for city life, but realized it didn't suit her and returned to the farm to pursue her calling. She has an eye for moneymaking and will often take on extra work to take in more money which she in turn uses to improve the farm. Sometimes she takes on more work than she can handle and things turn out badly for her. She and her sister get along well. She has a large extended family spread across Equestria. She is very physically strong. She doesn't like "girly" outfits or gatherings, and would prefer rodeos. She often acts as a level-headed voice of reason in discussions.
Amy Pond: Her parents disappeared sometime in her past, and she lives with her aunt. Her friends in school were Mels and Rory. After she met the Doctor as a child, she went through four psychiatrists and continued to draw pictures and role-play about him, silently obsessing over him her entire life. She eventually became engaged to Rory, but got cold feet on her wedding day and went off with the Doctor instead. She and Rory had a daughter, Melody. Amy then became infertile and divorced Rory because of how she believed he felt about her infertility. She remains loyal to Rory over the Doctor. She can be very hot-headed sometimes. She worked a few jobs such as a kissogram, model, and journalist.
Which of these two sounds like a more well-rounded character? In Applejack's case, there are distinct descriptions of "Applejack likes" or "Applejack wants", whereas Amy's is nothing more than a recitation of stuff that happened to her in the show. And it's not because I simply left out her likes and drives, they're just not there. If there's something that I'm missing that was explicitly shown or stated that Amy Pond likes or Amy Pond aspires to, please correct me. Until then, point goes to Applejack.
Round 2: Twilight Sparkle vs. River Song!
Twilight Sparkle: Twilight became Princess Celestia's personal pupil after she demonstrated great raw, but untrained magical power. She valued books and learning over social interaction, which caused Celestia to send her to Ponyville to learn how to make friends. Once there, she did make friends, but still remained highly engrossed in her studies. Now that she has friends, she's eager to learn more, however often does so "by the book" rather than immersing herself and learning through experience, leading to awkward social situations. She has severe OCD and obsesses over checklists, organization, and schedules. She fears what others think of her and is especially afraid of rejection by Celestia for screwing up.
River Song: River is the daughter of Amy and Rory, a proto-Time Lord named Melody Pond. She was kidnapped by the Silence and raised to assassinate the Doctor. However, when she attempted to kill him, she fell in love with him instead and gave him her remaining regenerations to save him. She became an archaeologist in order to follow the Doctor's exploits and had multiple offscreen adventures and romantic flings with him. Her obsession with him became so great that she was willing sacrifice the entire universe to prevent having to kill him. Later she met an earlier version of the Doctor who had not met her yet, and she sacrificed her life to save him so that he could go on to meet her in the future. River is sassy and flirtatious, and is usually a font of convenient knowledge, often outsmarting the Doctor himself. She wants to hide things from him so that his feelings aren't hurt.
River's a little better. She at least has "likes" (the Doctor), "wants" (the Doctor) and has "aspirations" (the Doctor). But she is still entirely defined by another character. Take the Doctor away, and who is she? Twilight also has her own person of interest, Celestia. But take Celestia away, and Twilight would still probably love books and studying, as she was shown loving these things even prior to meeting Celestia. Point goes to Twilight Sparkle.
Round 3: Fluttershy vs. Clara Oswald!
Fluttershy: Fluttershy came from Cloudsdale, but was constantly picked on because she wasn't very good at flying. Her fear of being taunted caused her to be afraid to ever try anything. By chance, she fell to earth and became friends with the woodland creatures, who wouldn't judge her. She then dedicated herself to taking care of animals in need, happy that she was finally able to do something with her life. She still has trouble with being assertive and often gets walked all over and ignored by others. She generally gives everyone the benefit of the doubt, but even she has her limits, and will assert herself if her friends or her animals are threatened.
Clara Oswald: Clara's mother instilled in her an interest in travel, however she died when Clara was 16. Clara was extremely attached to her and kept mementos of her that she adamantly refused to part with except under extreme circumstances. She decided to fulfill her dream of traveling and stopped to stay with a family friend along the way, however their mother died while she was there and she felt a responsibility to the children, so put her own plans on hold to stay behind as their nanny. When the Doctor appeared, he fulfilled her desire for travel, but she still insisted on periodically returning home to look after the kids. She was suspicious of the Doctor's motives for bringing her along, ultimately culminating in the revelation that she threw herself into the Doctor's time stream to save him at multiple points in his life.
Clara's doing a lot better here. Clara "wants" and "likes" things, AND has a distinct existence outside of her relationship to the Doctor. As Fluttershy is also not entirely defined by another pony and has her own distinct likes and desires, I'll call this one a tie, with one point apiece.
Final Score:
My Little Pony: 3
Moffat: 1
Again, this is NOT an attempt to say that the My Little Pony writers could write for Doctor Who. They're two completely different genres and target audiences, and I don't think it's an appropriate fit. This was ONLY a discussion of which show has the more organic and fleshed-out female characters, to back up my point of why I would not want Moffat writing a female Doctor.
If someone wants to defend Moffat's characterizations beyond "shut up, Moffat is a genius because he just is", I'd be glad to see that kind of analysis, because I simply can't see it. "Sexy" is not a character trait. "Feisty" is not a character trait in and of itself without an underlying driving reason. And "being a redhead", "being Scottish", and "being a girl" are not reasons; there needs to be some kind of underlying causal event or situation so we understand why this character is who she is. If My Little Pony can do it, surely Moffat can, too.