I have thought about it and decided that I prefer Classic Who, despite the improved production values, modernized pacing, and attractive actors in the new show. My reasons are outlined in above linked post (from my Who-themed Tumblr), but if you don’t feel like going there the short version is this: in the old show, despite the fanservice and screaming damsel in distress scenarios a lot of the female companions were put into, a show made in the crusty old sexist Sixties and Seventies was far more advanced in its consideration of female roles than the 21st century reboot.
Consider how many of the old female companions had real jobs and actual lives outside their travels in the Tardis. Liz Jones was a scientist. Romana was a Time Lady. Sarah Jane Smith was a journalist. (However: I cannot forgive Russell T. Davies for making her pine for the Doctor. Worry about him when he apparently didn’t contact her for years and years, yes — “I thought you were dead!” was quite a normal reaction. But then they went on to imply that she never lived a full life after ceasing to travel with the Doctor. Again, not necessarily a wrong reaction, only it plays into the whole idea that female companions can’t live whole lives outside of the Tardis. That is completely counter to the fact that the Doctor is a vagabond, that traveling with him is exciting but dangerous, and that people need to grow and change. Also people who don’t have the Doctor’s lifespan and ability to regenerate have no business foisting themselves for the rest of their lives on the man thank you ROES for telling the Doctor you’ll travel with him forever even though you know and he knows that humans don’t live forever and I can’t imagine the Doctor changing your adult diapers and pushing your wheelchair.
Anyway. Perhaps it’s just a different kind of sexism — Liz always wore those short skirts (though why shouldn’t she, she had smashing legs), Leela likewise was fanservice with a knife (NTTAWWT my fan was certainly serviced), Three did treat Jo like a child (but he also taught her things and let her do things and trusted her and she grew and changed and matured are humans are supposed to do, again compare with ROES, the universe-breaking stalker). The old who companions were strong women often put into damsel-in-distress situations, that is true. However, the “strong” women of New Who, with the exception of Martha who was always, always competent and only almost lost it once when the Doctor’s psycho ex-boyfriend kidnapped her family, but it was justified, are also often put in damsel-in-distress situations. But that’s not the big deal — that’s just par for the course in adventure shows. What is wrong is the way they are treated as characters as regards the Doctor: as needing him to feel whole and to become “real” people. It’s the whole cultural idea that women are incomplete as human beings until the associate themselves with a male, ideally to have his babies, but just being his adoring sidekick will do in the “enlightened” 21st century.
And please note the penalties for refusing this traditional role are severe. Not only did Martha end up being constantly disrespected by the Doctor, Donna was turned into a brain-damaged amnesiac. But Donna sought out the Doctor! you reply. Oh yeah. About that. She initially refused to travel with him, as you will recall in the Christmas special “The Runaway Bride” that introduced her. That sealed her fate: she was maneuvered by Dalek Caan into looking for the Doctor, and then ended up having to have most of her brain erased which basically put her back at square one personality- and life-wise.
There is one small saving grace: the Doctor is often shown as usually more or less befuddled that these women want to keep traveling with him and aren’t happy when he tries to give them back their human lives. Part of it is he now apparently hates himself. Another part of it is an awareness that he can’t keep humans like pets. Still, the way the companions are now being written makes it look like his taking them on is weird; if you know that their wanting to be around you isn’t good for them, why do you keep letting them on your Tardis?