I mean, Ten may have been hung up on Rose a bit after she was gone, but he eventually got over it and when given the opportunity to have her back he instead decided to give her up because it was for the best.
Eleven, for some reason, keeps going back to Amy long after her story was over, then pleads with her to not go after her husband whom he knows she loves more than anything.
And it just seems like the writing makes the idea of a normal life a little too easy for Amy and Rory. They are gone for months at a time, yet both don't get fired from their jobs. Not only that, Rory gets offered a promotion to full time. I'm not sure if I'm supposed to be feeling for them and their uncertainty of if they should leave the Doctor or not. What else about their lives is in an upheavel? It doesn't seem like much, so why even bring it up if being gone for months at a time does nothing more than make it hard for Amy to be a bridesmaid?
Of course, season seven did do something right in bringing in family members, but it was a little too late. Rory's dad should have been there a long time ago, and that, I think, is what makes me like the RTD era so much; the families. When The Doctor picked up a new companion, it wasn't just the companion he was getting, it as all the baggage of their whole life, and that's what I felt most drawn to. With Rose he got Jackie and Mickey along for the ride, with Martha he got her family's whole big dysfunctional mess while they were being lured into a trap by one of his enemies, and with Donna he got Sylvie and Wilfred.
And oh, how I absolutely adored Wilfred.
The Doctor didn't just affect the companions, he affected the people closest to them as well.
The Doctor changing the companions was a big theme in the RTD era as well. It was the basis for the "Children of Time" at the end of season four. Not to mention, it was a big reason why Donna's fate is so sad. Wilf tells The Doctor that she was better with him, because of the way he had changed her and given her a reason to believe in herself. It also went both ways. As you said, the companions all changed him as well, which I loved. It was a two way street.
I just feel like the Moffat era has been chock-full of brilliant concepts that never get properly executed. It's like he has so many ideas but isn't sure how to make them all fit so he just crams them in as tight as he can. All these brand new characters that we are never properly introduced to that are now suddenly so important. Lesbian detectives with one being a lizard is a cool concept, but I don't really feel like I know these two that well. I would have liked a proper intro. Them and the Sontaran, and the fat blue guy from season six. They just came out of nowhere.
And as far as NuWho companions, for me it goes Donna>Rose>Jack>Martha>Mickey>Rory>Amy. Don't know where to stick Clara yet.
And as far as Moffat episodes in the RTD era, while they were certainly good I don't hold them all up as better than the rest like so many people do. Episodes such as "The Impossible Planet"/"The Satan Pit," "Human Nature"/"Family of Blood," "Midnight," "Planet of the Ood," "42," "The Runaway Bride," "Partners in Crime," and "Turn Left" all stand out at the top of my head. Certainly "Empty Child"/"The Doctor Dances," "Blink," and "Silence in the Library"/"Forest of the Dead" were fabulous as well, but Moffat was just one of many great writers, not the end all be all of NuWho for me.