Um, no. A modern 4.5 inch gun or even the 5 inch guns on American ships definitely does not outgun or outrange a WW2 battleship.
The guns on HMS Dreadnought topped out at 22km. And that's assuming they hit what they were aiming at.
A modern MkVIII will go from 28km.
Now, the 15-inchers on the Bismarck would do it (~36km), as would the RN's 14in MkVII (~33km), but the MkVIIs would only fire 2rounds per minute, and the Bismarck's 15-inch guns could do 2.5rpm.
The MkVIII will manage 25rpm.
So what we're looking at is low-rate-of-fire with old targeting tech and all defence provided by armour, compared with high-rate-of-fire, state-of-the-art radar and sophisticated defensive armaments to shoot down incoming shells. Funnily enough, this is why ships carry fewer guns these days!
In an extreme-range engagement I'd probably take my chances on the ship which can lay down 10 times more ordnance in the first couple of minutes and use it's defensive weaponry to eliminate the incoming, subsonic shells.
Biting the hand that feeds IT
