The reason it's worse than other types of war/bombings is that the effects are lasting. There is radiation, all kinds of medical problems for those not directly killed and it's affects generations to come. It's not like 5 years after the war houses would spontaneously combust because of the fire-bombings back during the war, yet leukemia, cancers, and other effects persisted for many years. Then there is the extent of the damage. It's one thing to be able to run from a fire (although many could not), or be part of a building block bombed where some people survive and many are killed. The center of the "a-bomb" is much more "total annihilation". Wiping out a city that quickly with no way to run, warn others, etc, was just not something that was even imagined before it happened. I wonder about the people who can't understand why the Japanese feel so deeply about this, the reasons seem pretty obvious to me. Yes, fire-bombing was "bad" for the other side, but it wasn't anywhere near as instant or long-lasting. It's not just about what has the highest body count.
All that said, using the atomic bomb was the right thing to do back then. The japanese and their fighting spirit were famous for their tenacity and attacking even in suicide situations. The island campaign had shown this time and time again, and the allies were about to set food on the mainland. It was going to be bloody to say the least, or at least there was good reason to think it was going to be. Hindsight is always 2020 and maybe certain generals or government leaders were getting ready to overthrow the emperor's rule or surrender, but that couldn't be taken into account and bet on.