The Enterprise (i'm assuming the Constitution-class one--not a,b, d, or f. No letter) would win on paper. It has better armament, shields, and would be impervious to the conventional weaponry the Galactica has. Bullets, nuclear weapons, those things are obsolete technologies by the time of the Enterprise. The Enterprise has automatically tracking independant phaser bays and torpedoes that are designed to blast through such things; the Galactica has a hull that's falling apart and substandard weaponry even for its time period... the only reason it beat cylons is because the cylons were relying on electronic warfare over improved weapons capability.
In practice, however, The Galactica would win because of Deus ex Machina. That thing has a destiny from God, gentlemen.