Don't forget Rodney
HMS Rodney, the ship that sank the Bismark, fired a broadside of over 8 Tonnes every 45 seconds at a range of 22 miles. The first Battleship fitted with Radio Direction and radar range finding, I think your type 45 would in for a whopin. Although it would be able to run away....
The Nelson class had only one serious defect, being hopellely too slow, but at 23knotts they were as fast as that white elephant of all white elephants HMS Queen Elizabeth.
Oh and Rodney had an operational aircraft, a Shagbat. Catapult launched no less.
More than the Queen Elizabeth can boast