There was no legitimate military target at Nagasaki Ground Zero. There was a Catholic cathedral there that was the target in this residential area. And as to the firebombing of Dresden, we won't consider that a war crime only because the victors decided who to prosecute for war crimes.
Nagasaki wasn't the primary target that day.
Bock's Car first went to Kokura, the target the arsenal there, but found visual targeting wasn't possible due to weather. Nagasaki was the secondary, the target the port and shipbuilding facilities. Low on fuel, they found overcast skies, and tried radar, with a break in the clouds allowing visual targeting. When
Bock's Car landed, it didn't have enough fuel to taxi off the runway.
Fat Man fell about 1 and a half miles off target (2.4 km). This was the era of Norton bomb sights and gravity bombs. In generally, US WWII bombers were expected to deliver between 30% to maybe 35% (won't swear to this) within a 1,000 ft (305) radius of the target.
Fat Man ended up a little under 550 yards (500m) from Urakami Cathedral during mass.
It's perhaps worth nothing that Vannevar Bush, for years after the war, would wakeup screaming from nightmares about the burning of Tokyo. We don't hear much about the firebombing of Tokyo. Incendiary bombing and intentionally starting firestorms was common in WWII. Up 97,000 died from the firebombing of Tokyo. 25,000 died in Dresden.
From the safe vantage of hindsight, people can may make what arguments they will. There were military targets in both Tokyo and Dresden, and whether where the bombs fell in Dresden was a case of deliberate targeting or "close enough" for a firestorm I can't say. I've heard both claims. Just know that Dresden wasn't the only city that was firebombed in WWII, and Vannevar Bush had nightmares about the burning of Tokyo.
I will admit being biased. My father would have participated in Operation Downfall, as would have others I knew, including three uncles. The surrender of Japan made Operation Downfall unnecessary. As it happened, I knew a man who'd been in Nagasaki with the first Allied troops after surrender, and he described having hair loss and spots on his legs that were later attributed to radiation. Looking it up, that would have been on September 11, 1945.
Bock's Car dropped
Fat Man on August 9, 1945, so he would have arrived 33 days after the bombing.
Most of the above is probably more than anyone wanted to hear about Nagasaki and Dresden. History is what history is, and no amount of ink can change what was done, one way or the other. Make of Dresden what you will. Just know that Urakami Cathedral wasn't the target that August day in 1945.