Well, I just finished a rather leisurely Prince game with Charlemagne and I got about 11k - Winston Churchill. That's pretty typical. I've noticed that the thing which gets you high scores is not Space Race or Cultural Victories, but war. I once finished with about 16k in score as Julius Ceasar - I won the game diplomatically, through war. That is, I waged so much war that I eventually vassaled enough of the AIs to win with the UN vote.
It was a very hectic game, with me almost constantly at war or preparing for war. The only game I've ever had that was more warlike than that was as Tokugawa.
How do you win the tech race? On Prince? To tell you the truth, I've never had a problem being tech leader in a Prince game, so I can't really say what things can help you out. For a Philosophical or Industrious leader, I usually get me a nice Wonder-laden GP farm and settle GPs into it, then get Representation.
If I can't swing that, then I use Hereditary Rule to bust open the happy cap and still get lots of cities really really big, really really early. I use a Hybrid sort of system. I get GP farms and the occasional generic Specialist City, but I also use Cottages. Can't stress enough the use of Cottages under Free Speech powered by civilian buildings. If you don't acquire Towns after Liberalism, then you are going to lose a straight tech-on-tech competition. Not even obsolete has shown this to be false.
