Battleship Richelieu vs Roma, Who Would Have Won?

In my last thread, I gave the hypothetical situation, who would win, Richelieu or Bismarck/Tirpitz. Now that I see WGing pictures of Roma and Richelieu, it's time to ask, who would win, the Battleship Richelieu, or the Battleship Roma? Historically, the Richelieu class was built to counter the Italian Littorio class Battleships, however, she would not be completed until after the French Third Republic had fallen. These ships were built to fight each other for the fate of the Mediterranean, but it was not to be. The Richelieu would end up damaged by British Commandos, torpedoed by a Fairey Swordfish, would end up in a duel with a number of British capital ships, and would join the Allies to be refit in New York. However, the Richelieu's refit was only finished one month after the Roma was sunk by German bomb on September 9th, 1943. The Roma herself was stymied by a lack of fuel and escort ships, and became flagship for Regia Marina. Roma would end up harassed by by allied aircraft, taking damage from a Flying Fortress, until she met her fate against a German bomber. For the sake of argument, I'll entertain scenarios where a pre-refit Richelieu and Roma engage, or a post-refit Richelieu engages. I'm looking to see which ship had the better design, and frankly, I don't have access to the intrigue details of either ship, or Italian/French Naval doctrine. If you think it'll provide a more interesting scenario, you can give Richelieu her 284 P4 type gunnery radar. The battlefield will be the Mediterranean sea, both ships would be fully loaded with fuel and munitions. I'm interested to hear your insights into the matter. Who would win?