Family Guy wasn't cancelled half-way through it's first season. If it had been it might have gone the same way as The PJ's. Family Guy wasn't that funny at the start.

And it still isn't funny

Honestly, I just discovered Dr. Who last month. I bought all four box sets (Chris Eccleston and David Tennant) and watched them over a one week period (really, over four non-consecutive days). The show is absolutely amazing. It is a good change of pace from bounty hunter based sci-fi or military based sci-fi. Don't get me wrong. I still love Star Trek and Star Wars, but Dr. Who has earned a spot on my list of greatest sci-fi shows of all time. It is understandable if you aren't enthralled by Firefly, it is understandable. Dr. Who really raises the bar.

I loved firefly. I hated dr who. I watched a few episodes of both the old series and a newish one and they were both pretty crap imo.

As with everything, some episodes are better than others. If you ever feel like giving it another go, "The Girl In The Fireplace" and "Blink" are both well regarded. Indeed, Blink is practically stand alone, requiring no knowledge of the Doctor and a cracking story to boot.
The older the Dr Who is, the harder I find it to watch. It's actually fascinating to me how completely differently old episodes are structured.

It would probably help to start from the first episode of the new series, rather than to jump in at random between the old series and the new series. Conversely, you could try watching "The Waters of Mars." That is one of the best episodes of Dr. Who. You could also watch "Silence in the Library." That is a pretty good episode. But Dr. Who is not for everyone. It is a family show (not to be confused with being just for children) and has a rather low budget, since it airs on public British television (It is the BBC equivalent of a PBS show).

Stunning episode, but interestingly, the Doctor was almost not in that episode. My favorite of the new ones might have been "Human Nature/The Family of Blood". There are so many differing opinions on what makes Dr. Who great... some absolutely love the ones I just can't stand (or consider filler, at best).
Back on topic though, I loved Firefly, except for "Ariel". The blue hands guys stuff was completely out of style with the show. The humor in the show was excellent, and the acting was quite good - Summer Glau was somehow able to effectively play the innocent girl/frightening psychotic. Jane was just a hoot no matter what. And of course, Kaylee. Nuff said.
Check out the Complete Guide to Google Wave http://completewaveguide.com/ for some funny examples taken from Firefly.

One of the reasons that it's such a good introduction, i feel. A new watcher gets the "full Doctor" experience. It's hard not for a new watcher to connect with Sally Sparrow.

You can't really compare Firefly with Dr. Who and Red Dwarf. :)
While I can't really answer about why the series was considered so great by others, I can say why I think it was great:
-interesting and believable setting
-great choice of actors
-interesting mix of science fiction with the western genre
-it plays with and subverts various clichéd tropes
-interesting characters with well written and acted interactions
-(minor): almost always accurate portrayal of real newtonian physics in space
-very good soundtrack
-it had the potential to be a great series

Wasn't it? I thought it was a bit like The Simpsons: funny for the first few seasons, then going downhill in terms of humour and everything else.

Because the old ones were written for the British People, with long attention spans for long stories, and selling to American stations wasn't even an afterthought of the production, whereas the obverse is true for these "new" ones : Written exclusively for the American market, with their attendant goldfish memories, with shallow stories and bad acting (yes, even more horrible than the 1980s Doctors!) and over-ramped special effects.

See, I can't really agree with that. I think many older Dr Who serials would greatly benefit from tighter editing.
Which ironically is quite the opposite of how I feel about Season 5 of Doctor Who. They've squeezed some quite fantastic stories into one episode that would have benefitted greatly from some room to breathe.

@Lone3wolf
I knew it would be impossible to have a civilized conversation about Dr. Who, without some Briton coming in and taking it as an opportunity to "take the mickey" out of Americans (you guys still use that slang term, right?).
1) The special effects of the new Doctor Who are not really all that high end. They are by no means poor, but it is not overproduced in order to suit Americans. They aren't even top notch compared to what has been done on other shows. You are perhaps older and remember the less sophisticated effects of yesteryear. However, consider the fact that technology was far more limited in those days. If they had access to the tools of now, back then, it is reasonable to assume that they would have made the effects just as they do now. You can't compare limited technology to sufficiently advanced technology. It would be like comparing claymation to CGI. Not everyone chooses to be like Toei (the makers of Godzilla, who to this day, still use rubber-suit monsters).
2) Have you ever watched a season of House M.D., Bones, Dead Like Me? America is rife with programming that involves single episode stories that contribute to season long story arcs. What about (new) Battlestar Galactica? Granted it has a mixed cast (primarily American, British and Canadian), the series was created, developed and produced by Americans. It is one of the most noted shows to have surfaced on television in the last decade. Not all American programming is shallow. Don't get me wrong, we have plenty of horrific things in our pop culture (the current round of hip hop and pop music is absolutely deplorable) but that is not representative of our entire culture.
How do you feel when somebody makes an ignorant statement about all Britons having bad teeth (absolutely false, of course)? Or saying that you are an oppressed police state (though CCTV does seem very creepy and Orwellian)? We are all here as fans of nerdy things, be it science fiction or video games or fantasy etc. We should not reduce ourselves to petty bashing, even as a means of fostering a sense of nationalism (which everyone should take some pride in their respective country of origin). We all share a common ground. Let us focus on that, rather than focusing on assailing a nation over largely erroneous claims.

The current format of Doctor Who has nothing to do with appealing to the Americans. If this were true then all episodes would be 40 mins long to incorporate adverts. As it stands American viewers on BBCA have to catch the first run episode as every repeat after that is often cut horribly so they can put in the adverts. It was the BBC that decided on the new 13 episode roughly 45 min format. As for the style of the show that was chiefly the decision of Russel T Davies who is an unapologetic Joss Whedon and Buffy fan. Anyone who has been watching the new series 5 has seen a marked change in tone to both the show and The Doctor himself with new show runner Steven 'Blink' Moffat in charge.
For one thing we are safe in the knowledge we never, EVER have to see Rose again. RTD's Mary Sue.