If there are any alternate theories I'd really like to hear them, but honestly the way its presented here...something about it just makes sense. Some of the comments in that same page also do bring up a good point if you look back. The specific environment and circumstances throughout each regen does effect the succeeding one.
Let's look at the New Who Doctors:
War-9: Time War trauma as War caused 9 to start out embittered and shaken.
9-10: 9's adventures with Rose, specifically the Bad Wolf finale stuff, caused 10 to be more romantic towards companions, Rose especially.
10-11: 10 regenerating alone and unwilling caused 11 to be friendlier towards companions
11-12: Explained in the article.
One could make the case for Classic Doctors as well.
1-2: 1's crotchety behavior, supported by his last adventures defrosting a bit, caused 2 to be younger, happier, and sillier.
2-3: 2's trial and forced regeneration caused 3 to be more authoritarian
3-4: 3's time working in authority and straight sense of justice caused 4 to be a bit more anti-authority and slightly out there.
4-5: 4's longevity and the thing's he's seen, taking part in many stories, caused 5 to be the youngest at this point and be more of a pacifist
5-6: 5's kindness, willingness to save Peri, and the Spectrox, caused 6 to be madder, grander and more eager to throw himself into the fray. Also may or may not have something to do with Maxil shooting 5.
6-7: Not sure. If we go just by TV, we can't tell, so maybe we gotta wait for the Big Finish coming this year.
7-8: 7's chessmaster attitude, duplicity and guile, and possibly being alone in the TV movie, caused 8 to be romantic and full of life.
8-War: Stuff that happens in Big Finish, plus the events of Night of the Doctor.
There's a bit of a problem in the first episode that introduces the Ninth Doctor and that starts the new series. In there, when he sees himself in the mirror, he makes a remark about the ears. People take it that Nine has just newly regenerated (in hindsight, just after the events of the Time War shown in The Day of the Doctor). Yet we also see in Rose that the Ninth Doctor has shown up all over the place in human history--which suggests that Nine has been around for a very long time.
My solution to this seeming contradiction is that, when we first see the Doctor, he has newly regenerated. At some point during the Rose episode, when he's not on screen, Nine has gone off in the TARDIS and had a bit of a grand tour of space-time [this seems like something that each new regeneration does at both the beginning and the end of his cycle]. So later in the same episode, a lot of time has passed for the Doctor, while little has passed for Rose.