There are countless opinions on the difference between classic Doctor Who and new Doctor Who, but once you get past all the technical aspects, the period specific stuff, and the differences in the society it was created for, it seems to me that the main difference is that old Who was about people in crisis, with the Doctor acting as a catalyst to change the situation, where as new Who, specifically Moffat Who, is all about the Doctor.
I think it's fair to say that a lot of the time in the original series there was too little Doctor, with virtually no background given to the character until the series had been running for ten seasons, and the TARDIS, that wonderful place, often serving no function other than transporting the characters from story to story. But in Moffat Who it seems like everything is about the Doctor. The tedious season-long story arcs are all focussed on the Doctor, seemingly intent on probing mysteries to which nobody really wants to know the answer. There was even an episode that consisted of little more than characters wandering around the TARDIS, which, apart from a few nice moments, served to make it less interesting than it had been when it was all a mystery.
New Who has now reached the opposite extreme from the early days of old Who, when what would work so much better is a lot closer to the mid-point between the two. Neither a complete absence of Doctor stuff, nor a total fetishistic obsession with the character. I only hope that the next person who is put in charge of the show has some understanding of this.