Speaking for myself only, I prefer the original because the characters didn't wallow in emotions all the time. Sure, they had been through the destruction of their society, but, they picked themselves up and got on with the business of living [I]like real people would do.
There are some real people from New York City and Northern New Jersey that I believe may have a different perspective on how long it takes to get over a horrific attack. In addition, after 911, the terrorists were not continuing to attack the city, as the Cyclons in that fictional Universe continued to chase and attack the fleet. And the rest of humanity outside of NYC had not been wiped out!
There were no Mudd's Women or Tribbles episodes, but this was a different type of show.
I think it is pretty much accepted that the dark tone of nBSG was influenced by the events of 911. The series might not have even connected well with so many if it had been produced before the attacks. Given the premise and the length o f time covered by the story, I think things would actually be pretty dark. Also, the trend to add on-going soap opera story lines into 'primetime' dramas hadn't become a trend yet back in the 1970s, although I would say the original was more of a family show, and nBSG was geared more toward adults and away from kids.
This is opposed to the tone of the original series in which we find in the episode immediately following the destruction of the Colonies Starbuck and the gang partying down and having fun on a casino planet (well, at least until they start getting eaten....!).