A heavy cruiser versus a modern warship at gun range

Would a World War II heavy cruiser be more heavily armed and destructive than a modern comparable warship?

At gun range the comparison becomes very dangerous for both, and an armoured cruiser may have advantages that long-range missile comparisons obscure.

Range and scenario matter more here than declaring one era automatically superior. Neither an Alaska-class cruiser nor Zumwalt would be pleasant to face at gun range, and a County-class cruiser could be more powerful than a Type 45 in that narrowly defined circumstance. A modern escort may expend its limited anti-ship missiles without defeating armour that those warheads were not designed to penetrate. Because the scenario begins inside gun range, the cruiser can launch heavy shells while the modern ship fires its missiles. Even an armour-piercing shell that fails to detonate may pass through a lightly protected hull, open large holes, and create a severe flooding problem. Missile and sensor reach matter differently once the artificial gun-range premise is removed.