Can we compare and contrast the two series. I'd love to see a discussion about which series did what "better." The science was laughable in TOS but there were aspects of that series I liked alot.
I think I had watched nuBSG about half a dozen times continuously then took a complete break from it for 3 years so here's some thoughts and hopefully memory serves me correctly.
Music. The soundtrack from nuBSG was cinematic in feel and tone. I loved the use of unusual and little used instrument and of course traditional western orchestral pieces fitted in with the series. Of course there is the famous Cylon motif that was used to amazing effect on numerous scene. There is hardly any music on ST apart from on opening titles.
Visual style. I believe nuBSG was mostly shot in digital which gave a sharp crisp look especially of the insides of the Galactica which was lit to give an almost clinical sterile feel. I also liked the zooming hand-held shooting style which gave it a naturalistic, documentary feel. Michael Rymer who directed the most number of episodes and was also a producer of the show brought a cinematic feel to the show and produced great images like Number 6 in a red dress. For most of the ST series, while the sets and SFX were amazing, the visual style never really caught me.
Acting. nuBSG has such a great ensemble of actors. The senior members Edward James Olmos, Mary McDonnell & Michael Hogan played well against the younger actors like Jamie Bamber, Katee Sackhoff and James Callis. I quite liked the younger members of the cast that gave the show a fresh feel in contrast to the older and experienced actors. As mentioned earlier, Rymer brought a cinematic style and feel to the show and allowed the actors to play out scenes. In contrast the ST was a very grounded in the TV medium and while there was good actors and actresses in the show, they never really got to shine apart from certain episodes like the one I had enjoyed, the Inner light in TNG.
Writing. Obviously nuBSG was focused on continuous multi-story arcs and little standalone episodes compared to most ST series. What I did like was the dialogue, full of memorable quotes and speeches which highlighted the literacy of the actors. Examples of this was the foxes swimming out to sea monologue by Adama taken from the book Sometimes a Great Notion which was also the name of the episode, the "bodies upon the gears" speech by Tyrol on New Caprica which again was based on a famous speech by an American 60's activist and the Adama monologue on the separation of the police and the military. There was no much like that on ST.
Themes. The most obvious one is how dark the themes were. The nearest to nuBSG is of course DS9. However, even with these two shows, there was a difference. With nuBSG, rage, anger, grief, violence and desperation was explored where we see for example sanctioned torture and leaders seriously contemplating 'disappearing' opponents. With DS9, it was more philosophical where ethical lines of the federation were being blurred in the face of defeat by the Dominion.
Realism. I know both are Sci-fi programmes but with nuBSG, in the mini-series and first season at least, you got a feel of the lives of the crewman aboard with members of the crew being called to duty through the tannoy, monotonous repetitions of SitReps and even events seen by us as fantastic like jumping to FTL is treated by members of the crew sitting bored chewing gum. In contrast, there is only glimpses of the day to day routine of the crew, one which I had mentioned in the Starship Captains thread in the TNG forum.
Non-Humans. In nuBSG, apart from the Cylons there was only humans and in a self contained story that worked. In ST, we have multiple non-human species and I like that as their culture and society are explored.
Misc. I love the ambiguity of the themes and individual scenes in nuBSG that were open to interpretation. An example of this is the scene in the miniseries where Caprica 6 kills the wean before the Cylon nuclear attack on Caprica. Taken literally, it is a vile and shocking scene but after the act, she is shown with anguish and distraught over her face. You could interpret it as she was fully aware of the act she had committed but had done so because she knew the child would suffer a slow painful horrible death in the oncoming attack and the fact that we find out later on that Cylons are desperate to having children of their own but unable to. Also, the ambiguity of the One True God and the Cylon religion can be used to explain the Deus Ex machina at the end, well at least to make it watchable. Again, there is very little of that in ST.