Although I don't think it was until O'Neil's tenure on Batman that the difference started to emerge. In the Golden and Silver Ages, Metropolis and Gotham weren't that different. If anything, judging from the early comics and radio series, late-'30s and early-'40s Metropolis was a worse hotbed of corruption and organized crime than Gotham City, since Batman and Robin began working openly with Commissioner Gordon and the GCPD as respected allies in law enforcement while Superman was still a subversive vigilante on the run from the unreliable police. And otherwise, both cities were portrayed as pretty similar throughout the '40s-'60s, first as gritty, crime-ridden, politically corrupt cities that cried out for two-fisted vigilante justice, and later as bright, cheery fantasy settings where avuncular, wisecracking superheroes dealt with flamboyant robbers and alien visitors and romantic entanglements and absurd transformations. George Reeves's Metropolis on TV recapitulated the evolution of the comics version, starting out noirish and crime-ridden in black-and-white but becoming more bright and fanciful in color, while Adam West's Gotham City was always a happy, bustling urban paradise except when it was threatened by diabolical costumed fiends.
I think the reason Gotham got darker in the Bronze Age is that after the Adam West series, the Batman comics made a deliberate effort to get more serious and gritty as a counterreaction to the show's goofy image, while the Superman comics were under no such pressure to change their tone.
