With Christopher Eccleston, he was just getting over finishing the time war and destroying Gallifrey, which he stated was a big part of his character development for the 9th doctor's demeanor. With Rose, she calms him down a bit as the human balance of conscience after the time war.
I imagine, with what happens at the end of Tennant's series, you can see that while Matt's doctor is generally happy on the outside, when you watch it again you do notice how much he actually does seriously flip out at things. He's actually a lot more vengeful and does start to show signs of the post traumatic stress he's been through more. He has a lot more emotional outbursts, like in the episode with the weeping angles where Amy is in the forest and he just snaps not knowing what to do..
The new series starts on Saturday anyway, shame that Amy's leaving after the first half of the series..Will be interesting to see how that comes about and if it would be the end of River too.