CounterAttack said:
To me, Tennant seems more likely to think outside the box and come up with ways to deal with an issue, where Eccleston, despite the Doctor being a pacifist through and through, kind of looks and acts more like a soldier than a Time Lord.
This comment annoys me somewhat, because 9 kind of just got back from war (it's even implied that he was a general), let alone the one that killed off his entire race. Of course he acts like a soldier!
Also, 3 was extremely militaristic and got into fights all the time. 2 didn't hesitate to steer an army into a sun in one episode. 4 (and he's
the Doctor) has tried to wipe out the Daleks on one occasion. And 6 was extremely bipolar and violent.
Where I'm going with this is that the Doctor (as a collective) isn't a pacifist so much as a righteous man. Each one has a different way of going about bringing about the greater good. Tennant was more of a 'take a third option' kind of person, always finding or attempting to find a peaceful resolution that ends well for everybody (unless you count the Family of Blood).
I personally love Matt Smith, but I think most peoples' beef with the new series is not so much the actors (unless you're shallow enough to just want Tennant eye candy) but more the new direction it's been taken by Stephen Moffatt. Not only is it darker and grittier (in terms of the the cinematography at least), not only has the story pretty much gone 'forget the first 4 seasons never happened', but the way Doctor Who is presented has changed (and
definitely in the new season).
For example, the story has become less about a mishmash of ideas and motifs than it has become part of a massive overarching plot. In Seasons 1 through 4, there were allusions to the finale (in order: Bad Wolf, Torchwood, Mr. Saxon and Pretty Much Everything) but they never got in the way of the segregated stories. In 5, the season became increasingly more dominated by the cracks, building up to (rather than alluding to) a big climax. In 6, aside from the Pirates episode (which was the worst so far IMO) it has been almost entirely about the grander scheme. 11's death, River Song and the war in the Doctor's future have taken centre stage, and the shift in storytelling method is definitely irritating people, whether they're aware of it or not.
Doctor Who isn't new to this - the most famous Doctor Who story was the Key to Time arc - so this isn't necessarily a bad thing. However, it also means that we'll need to see this story reach its conclusion to achieve a solid verdict as opposed to taking smaller stories in bite size chunks.
Anyway, I could go on this massive TL;DR essay about Doctor Who and its shifting storytelling and how it affects reception, but that might just have to wait for another day. Needless to say, that up there is a good chunk of my answer to the OP's question.