Well, there's a few reasons.

Some facts on the bombing, before we get into it:

The claim of up to 250,000 casualties made by British historian David Irving who later gained notoriety as a Holocaust denier after the 1963 publication of his book The Destruction of Dresden was shown to rely on a report doctored during the war by the German propaganda ministry. And in considering the stories of eyewitnesses who recalled seeing the center of Dresden covered with bodies, one must bear in mind that the city center is a relatively compact area of no more than eight square miles; even 10,000 bodies in such a space would have been an appalling sight. Based on the most reliable numbers available, it is reasonable to conclude that the final death toll was in the vicinity of 25,000. Tens of thousands of others were wounded or made homeless.^^1

Now, in comparison, here are some facts on Hiroshima:

...the descending bomb exploded, instantly converting the city of more than 300,000 inhabitants into an atomic furnace in which approximately 80,000 people were instantly killed and at least 160,000 more were injured by blast, fire, or radiation.^^2

But don't get me wrong: this isn't the "death toll" Olympics. That's not the point I'm trying to make. After all:

In terms of lives lost and damage done, the Dresden raid was less destructive than the now largely forgotten American air attack on Tokyo on the night of March 9-10, 1945, which killed 100,000 Japanese.^^3

So...why don't we remember Dresden and the Tokyo bombings?

Well, firebombing of cities was not anything new. The world had already witnessed the dramatic power of firebombing. That didn't surprise anyone. However, the atomic bomb is a whole other ball-game.

Consider this: In Tokyo, they had to use 330 B-29's dropping 2,000 tons of incendiaries to kill 100,000 people and destroy 267,000 buildings.

Hiroshima, on the other hand, was a completely new type of weapon. It was far more destructive than people believed it could be, at least in the form of one relatively small bomb. Three B-29s (if memory serves) carried a bomb that killed 80,000 people or so instantly and destroyed 69% of the buildings in the city, a total of 62,000.

Let that sink in for a moment. One bomb, one relatively small bomb, killed 3 times as many people as died in Dresden, in one moment. And in Dresden, they'd had waves and bombers over the course of two days.

Knowing that, culture easily seized on this new weapon. It became (and still is, though in new forms) the most destructive man-made force in the world. Firebombs require huge waves of attack; this requires just a carrier, and an escort at best. This was unlike anything ever seen before. Buildings flattened, vaporized, or destroyed, people vaporized, burned alive, or killed by pure blast force, and all with one bomb.

Knowing that, is it any surprise that we remember it so much better?

^^1 Sifting Dresden's Ashes Tami Davis Biddle The Wilson Quarterly (1976-) , Vol. 29, No. 2 (Spring, 2005) , pp. 60-80

^^2 Hiroshima in Retrospect Hugh M. Gloster Phylon (1940-1956) , Vol. 17, No. 3 (3rd Qtr., 1956) , pp. 271-278

^^3 Biddle again

Here's one more take, as someone who nuclear history but who spends a lot of time trying to get people to think more about the US firebombing policy — which was so much more ruinous against Japan than the two atomic bombings.

Debating the atomic bombings appears to present interesting and novel questions. They are usually framed in this fashion: "Was the use of the atomic bomb justified? Let's weigh the deaths of many civilians against the survival of many soldiers, knowing that the atomic bomb ended the war rather quickly."

From an historical point of view, this is a terrible framing. The "decision" to use the bomb wasn't based on this kind of calculus; the bomb was just one of the last of many decisions to deliberately target civilians; the people who dropped the bomb had no clue whether it would actually end the war; the invasion itself was not scheduled for several months later; it still isn't clear whether the atomic bomb, as opposed to other factors (i.e. the Soviet invasion of Manchuria) which caused Japan to surrender; etc. etc. Framing the debate in these narrow terms actually assumes answers to rather thorny historical questions.

How does one frame a discussion of the firebombing? The way I like to put it is: "Under what conditions is the deliberate burning of tens of thousands of civilians an acceptable policy by a state at war?" Now that gets to be a thorny, very less neat question right out of the get go. (And it in fact still applies to the atomic bombings just as well.) Generally speaking, people don't want to have that conversation. They don't want to generalize these policies outside of the nice, apparently neat box of "the end of the Pacific War with Japan's surrender assured." It isn't as fun to talk about. It doesn't contrast glorious technological achievement with seemingly tough political decisions. It's a dark question. It deals with a mundane technology — jellied gasoline cluster bombs deliberately developed to destroy civilian houses — rather than a story of scientific glory and clever physicists and secret laboratories.

Then you add to it that the story of nuclear weapons begins with Hiroshima and Nagasaki, it doesn't end there. They become portents for future problems and questions. They become signs of things maybe to come. Whereas napalm — napalm stays napalm. It doesn't disappear (it makes a resurgence in Vietnam), but nobody worries about it. Because nobody is going to drop napalm on the United States. But other people might drop atomic bombs on us. Which points at the other fascination with the bomb: Americans immediately imagined our bombs being used against ourselves (and took the Hiroshima damage map and superimposed it on our own cities). Did we do the same for firebombs? I've only seen one visual (created by the US Army Air Forces to brag about their effectiveness in firebombing Japan) that implies this connection — and it's unusual. Generally speaking, we don't imagine this sort of thing happening to us. We do with the atomic bomb. It makes a big difference, I believe.

Since this is a somewhat wooly and wild response, I will add one important reference: if you are curious why the atomic bombs have occupied such a strong place in American historical memory and imagination, Spencer Weart's Nuclear Fear: A History of Images (Harvard University Press, 1986) is a wonderful, insightful read.

You hear so much about Hiroshima specifically because it was an atomic attack, and the beginning of atomic warfare heralded an entire new era of human history. The development of nuclear weaponry following the attacks on Hiroshima and Nagasaki was incredibly influential throughout the cold war and to today.

Dresden, while a devastating attack in its own right, utilized conventional incendiary weaponry. Really it is famous because of the seeming callousness of targeting a civilian city with debatable military value (there's some debate on this). Also, the atomic attacks on Japan led directly to Japan's surrender, whereas the bombing of German cities hastened, but did not cause, German defeat.

The book you're reading is likely Slaughterhouse Five, which is a great book and, in its own weird way, a primary source on the attacks on Dresden. Author Kurt Vonnegut was there, and much of the book is based off of his experiences.