Below is all just my opinion. Read at your own risk
I so disagree with the decline after Moffat took over! The show got much more enjoyable to me after Matt Smith came in. I was glad to see manic/mopey Tennant go, along with his awful sidekicks (Catherine Tate excepted). Season five was the most mature to me, it always felt a bit too much like a kids' show before that. There's still stuff I don't/didn't like in season five and six but not as groanworthy as loads of stuff in two-four.
I have to admit I've only seen the episodes once and can't call out any specific examples, it's more a general feeling. Rose didn't do anything for me, bad acting didn't help either - although Mickey was even worse. Then we got Martha Jones, who's only job was to want the Doctor to fall in love with her, while he was still pining for Rose. Donna at least had some character, even if it was a tad annoying at the start, and she had a real character arc.
Lastly, I think Smith's the better actor, or at least has better range. Tennant could do angry and sad, but Smith can do wonder, glee and looks like he's enjoying himself much more.
I'll be in my panic room now
Scientists are predicting the future will be much more futuristic than originally predicted