“It’s always [the companion’s] story. It was Rose Tyler’s story, it’s Amy Pond’s story – the story of the time they knew the Doctor and how that began, how it developed and how it ended,” Steven Moffat told BBC America, ”The story begins again, not so much with the new Doctor, but with the new companion. The Doctor’s the hero, but they’re the main character.”
I think this is a crucial difference between the Russell T Davies era and the Moffat era of Doctor Who (and indeed the difference between the William Hartnell era and the Jon Pertwee one).
Where RTD wrote the companion as the Doctor’s heroic equal (or at least someone who will acheive his equal by the end of the season), Moffat writes the Doctor as the hero of the story, and everyone else, including Amy, becomes a supporting character.
In RTD’s era, Rose, Martha, and Donna can be compared to the Doctor in their bravery and intelligence, and contribution to saving the universe. All three of those women saved the universe on an enormous, epic scale, in partnership with the Doctor, by the end of the season. I believe Davies wrote the companions with this intent. This is how you balance out the potential sexist element of the show.
See, the problem with Doctor Who, is that the main character is a dude, and his “assistant” is a woman. The marginalized group becomes a damsel in distress or just someone to “wow” at the Doctor’s intelligence. Davies countered this by making his three main companions’ journeys build up to moments of braveness where the Doctor became the “damsel” (surrounded by Daleks, captured by the Master, or locked up by Davros). This served to remove gender from the “hero” role.
In Moffat’s Doctor Who, the Doctor is the sole hero, and everyone else plays second

Does Rory play second fiddle to Amy's second fiddle? Uh...third fiddle?
fiddle. EVERYONE. We’re not meant to view Amy as being on a potential even playing field to the Doctor the way Davies intended. Instead of an equivelent to the Doctor, Amy is meant to be seen beside Rory, River, and Craig.
There are problems with this format, however. The male companions don’t get half the attention that the female companions receive. River and Amy are far more important than Rory and Craig, who only get to star, arguably, in about three episodes combined. Even after a whole season in the TARDIS, Rory only once got to outshine Amy (“The Girl Who Waited”).
On the whole, we think of the Doctor and Amy as the stars of this show, but Amy has yet to truly outshine the Doctor. Yeah, she has a few minor wins early on (“The Beast Below”/”Victory of the Daleks”), but they’re weak, and minor, compared to the Doctor’s season finale blow-outs. The problem is that the traditionally marginalized group (women) is always going to be the “assistant” in Moffat’s format. The women are always going to be a little bit less wonderful than the staring male.
In “Meanwhile in the TARDIS”, the Doctor refers to himself as “Space Gandalf”. Well, this is true, but more so back in the day. In the original 60′s Doctor Who, the Doctor was truly Space Gandalf, serving as the magical genius vessel who moves the story and exposition. But in Tolkien’s story, Bilbo is the hero. Frodo is the hero. Gandalf isn’t the hero. Davies Doctor Who was also closer to this format. The Doctor is a hero, he is magical and wonderful, but he’s really the vessel for the journey through which the companion becomes the hero.
But it seems Moffat is more interested in sticking to the Jon Pertwee/Tom Baker style Doctor Who, in which the Doctor is the hero, and although the companion is who we experience the story through, they will never acheive true heroism.

Ian and Barbara, the original Doctor Who companions
So what can be done about this? How can we make the dynamic between hero and civilian less gendered in Moffat’s format? Well, I think Moffat’s Who could seriously benefit from more attention to the male companion. Its been done before, in the 60s Doctor Who; Ian and Barbara were very much equals as companions, and both had their chances to shine. If Rory and Amy were on an even playing field, we might be able to see the Doctor as less gendered.
Alternatively, a female Doctor is going to make a world of difference. The fact is, you can’t consistently cast the marginalized group as the “lesser” of the two leads without it coming across as a comment on gender.
Where Davies’ Who said, “the Doctor is a brilliant dude, but his female friends, with a bit of practice, can be just as brilliant.” Moffat’s Who says, “the Doctor is a brilliant dude, and his girlfriends think he’s awesome for it.” I wonder if this problem was born out of a misinterpretation of Davies’ Who on Moffat’s part? Perhaps if Moffat had started Doctor Who back in 2005, we’d have had two companions from the get go, without the Davies’ imposed Doctor/companion format. Either way, we need a change. Let Gandalf be Gandalf. Let the woman be the hero.