One of the things I find interesting about NEPTUNE is the relative paucity of actual warships - destroyer and larger combatants - compared to Operation FORAGER, the invasion of Saipan, which happened later in June.
NEPTUNE had a total of 6 battleships - 3 American, 3 British. And the American battleships - USS Arkansas, USS Texas, and USS Nevada - were 3 of the 4 oldest battleships the USN had. (USS New York was conducting training in the States)
Nimitz sent FOURTEEN battleships to the FORAGER party. Granted, some of those were the fast battleships that spent a chunk of their time playing air defender for the carriers, but IIRC there were still eight of the older, pre-war battlewagons whose main job was shore bombardment.
Now, one thing OVERLORD had was that the landing areas were within range of land based aircraft, including the heavies from 8th AF and Bomber Command. While naval gunfire excelled at putting sustained bombardment on a target, the heavies couldn't be beat for putting a huge amount of explosives on a target in a very short period of time.