I'd have to say the Battlestar Galactica would win in a one-on-one battle:
While the Galactica is an old and very beat up ship, it's crew is made up of very battle-hardened warriors that have spent years fighting a much superior foe. They fight strategically and with everything they've got at their disposal. Your typical star destroyer is usually run by a bunch of bickering minion incompetents who are overconfident of their crew and ship's capabilities....they've also never faced any real challenge until the rebellion in the original trilogy.
The star destroyer would be an easy target for the Galactica.....