Russel T Davies has certainly changed Doctor Who, though several of changes are in keeping with story telling on TV at the present.
Several of the stories appear shorter, with no 'cliffhangers' as were present in the original series that was broadcast till 1989, however elements of these cliffhangers remain. There is the 'teaser' prior to the credits which acts as a mini-cliffhanger into the stories and in the case of the two part episodes still a cliffhanger present.
Doctor Who post-2005 has been said to be more Earth-centric with more stories being set on Earth in familiar settings, however this was also the style three seasons in the 1970s, where third Doctor (as portrayed by Jon Pertwee) was exiled to Earth, thus a majority of those stories were set on Earth, with a surrogate 'family' of support characters in addition to the familiar Doctor and companion grouping.
Russell T Davies as executive producer and head writer lead to many changes and developments in the style of the show, but many of these changes reflect story telling on TV in the 21st century. Modern CG graphics (which were already in use during the 1980s during which they were used in Doctor Who), more character based stories; the character of Rose and subsequent companions had far greater focus than previous companions (however, the character of Ace during the 1980s had a character development arc similar to modern Doctor Who), additionally there has been further funding and development into the new series of Doctor Who than was spent in the latter days of the Doctor Who's original broadcast.
Doctor Who has become not just a TV show, but a global brand with expectations to meet said brand, however this cannot be laid at Russell T Davies feet, BBC Worldwide is in charge of Doctor Whos commercial prospects and there are several other elements of the BBC in charge of other elements of the Doctor Who.
Doctor Who has changed and developed as new producers (or executive producers) have come and gone with the series developing as new creative teams entered the fray or departed.
Aside from formatting, and a general updating of certain elements such as special effects, the series remains at its core the same as it was in 1963 and in 1989. Where Davies succeeded was that he was able to update the show without having to reimagine it (like Battlestar Galactica) or by updating things so drastically you can't recognize it. And the high ratings, the rockstar-like fan reaction to the actors, and ever-increasing number of awards the show is receiving in the UK speak to the outcome of Davies' efforts.
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