The Default rules show the battleship to be the better unit. However, in real life, the BB would never get close to the CG, thanks to it's missile defense system. Even the 24 mile range of those huge guns is a pittance compared to the 250 mile range of the CG's offensive missiles. The BB has little in the way of defense, other than it's massive armor, whereas the few missiles it carries would be easily shot down.
I have changed my game rules to reflect this reality. First, I gave everyone decent stats. The BB is still the toughest unit of the two, but there's a couple of important divergences from the default rules. Both units can bombard. The BB can bombard at a range of 3, and with power equalled only by the Stealth Bomber. The CG has a bombard range of 8, and travels a little faster.
In a gunnery duel, the BB will beat the CG most of the time. But the CG wins when it can use its bombardment capability to cripple or sink the BB from a distance. It's greater number of MP's give it more shots too. Good chance of winning. It's still all in who gets to attack first, though. The CG has an edge in that it can attack from further away, but you still have to have good recon by other units.
I even have BB (and DD) upgrade to CG. That was mostly to reduce the size of the build queue, but who still has BB's? Not us.
DDs are useful for their speed and ability to upgrade from Ironclad (in my mod). Cheapness ensures I have a DD on station at most trouble spots by the time I can crank out enough BB's to do anything useful.
You may have a hard-to-kill unit in the BB (or CG), but it can't be everywhere. DD's let you spread your power out to engage the enemy where he is least prepared. Better to strike everywhere than 1 place.