Playing Civ 5 Gods and Kings I won a grand total of one game on Diety on a regular sized map or larger, and it was after multiple tries on a particular setup (Babylon, marathon, large map archipelago, beat everyone to frigates/privateers, domination).
Playing Civ 6 I won at diety my very first try. Germany, regular speed, regular size inland sea. Spawned in between Sumeria and Scythia. Rushed to archers, built 4, and took out Sumeria and a city state. Built total of 8 cities in a reasonable grid while defending against a DOW from Scythia. Ran to apprenticeship then industrialization. Got the Factory network going and got knights and siege towers. Took one city from Scythia with this but that was it. By then the Hansa machine was in full gear though. Built campuses everywhere, and fairly quickly went from 6th in science to 1st. Rushed to Combustion, saved $$$, and instantly upgraded 8 knights to tanks. Tanks plus siege towers. LOL. Down went Scythia, down went China, down went Rome. Kongo and Arabia, however, pulled out mech infantry armies (this is ~turn 250). So back to the bait shop. Science per turn was now well ahead of everyone else, so just rushed to composites, and fission, while again saving $$$. Instant upgrade of tank armies to modern armor armies. Modern armor armies plus siege towers. LOLOLOLOL. Game over before turn 290. Score was only about 1100. Funniest sight: a modern armor unit that I had sent out to scout and find Brazil getting swarmed by barb mech infantry. Other interesting aside: I never even bothered getting a religion. Instead, my territory ended up being the playing field for a huge religious war between Scythia and Arabia and Brazil, which none of them really won, so no one got close to a religious victory.
Next question is how to win at this level with another civ, and can it be done peacefully.