In many respects for the better, to be honest. At least as someone who is from the U.S., Doctor Who was fairly obscure and being a Doctor Who fan was sort of unusual. These days, Doctor Who is downright mainstream. Random strangers have some idea what the show is about, as opposed to confused comments about a guy with a long scarf.
For me, what is probably the most striking change is the media itself. These days, we have the ability to watch any given episode of Doctor Who, streaming them on our televisions or tablets or computers or even phones. We have so much access to Doctor Who and a vast number of other television shows and movies and other kinds of programming.
Seriously, it's mind boggling.
When I first got into Doctor Who, my two sources of it were reruns on PBS and Target Books, which doesn't have anything to with the big box stores to the best of my knowledge.
Which put me in the weird situation of having a near encyclopedic knowledge of almost every serial in the original series but only because I had read the books. My entire understanding and concept of the Hartnell and Troughton Doctors were from the books.
And the vast majority of the books were just transcriptions of the scripts. Some of the earliest written ones were even simplifications of the scripts. We're not talking great literature here.
And they still helped me become a dedicated Doctor Who fan :D The formula of whimsy and horror and fantasy was still there. Doctor Who, by focusing on a single eccentric outsider, manages to combine the intimacy of one person's actions with the vastness of time and space.
These days, Doctor is more accessible and has vastly better special effects. At the same time, it is still the quirky and disturbing adventures of a tragic, comic madman in a box.