It is my understanding that the Luftwaffe had difficulty inflicting mass civilian casualties in London early in the war, but as the war wore on and the Allies, looking to damage or destroy enemy factories, began to bomb cities like Dresden and Tokyo, they inflicted massive casualties. What allowed the Allies to cause such devastation ostensibly by accident where the Axis had failed to do so on purpose?
edit: reworded to address concerns over the Allies' intentions
For the most part, it's just a matter of scale. The Luftwaffe's primary focus was tactical support of the army; its first Chief of Air Staff, Walther Wever, had ordered long range four-engined bombers in 1935, but following his death in 1936 the orders were cancelled and production switched to larger numbers of tactical aircraft. That said, it was still the largest air force in 1940, with 1,380 bombers (mainly the Heinkel He 111, Dornier Do 17 and Junkers Ju 88) in front-line units in July 1940, and being able to fly from France meant the shorter range of twin-engine aircraft wasn't an issue. The heaviest Luftwaffe raids of The Blitz featured around 500 aircraft, sometimes flying multiple sorties, each carrying a typical bomb load of between 1,000 and 2,000kg.
The RAF was intended to have an offensive strategic role, but rearmament in the late 1930s had wisely focused on air defence and thus Fighter Command, so in July 1940 Bomber Command only had about 560 bombers including the obsolescent Fairy Battle, the heavier types (the Handley Page Hampden, Armstrong Whitworth Whitley and Vickers Wellington) able to carry a bomb load of up to 4,000lb, depending on range. With early war experiences rapidly demonstrating the vulnerability of unescorted bombers the RAF switched to night raids, but lacking training or equipment in this role accuracy was minimal, the Butt Report of 1941 concluding that only one in four aircraft over Germany managed to land bombs within five miles of the target.
After the threat of invasion receded following the Battle of Britain and the German invasion of Russia, strategic bombing was one of the few ways for Britain to strike at Germany so considerable resources were put into building up Bomber Command. Heavy four-engine bombers came into service, primarily the Avro Lancaster but also the Handley Page Halifax and Short Stirling, capable of carrying bomb loads up to 14,000lb (or in extreme cases a modified Lancaster could carry a single 22,000lb "Grand Slam" bomb), and navigational aids and specialist Pathfinder units improved accuracy. In 1942 Bomber Command famously flew its first Thousand Bomber Raid, though there was an element of propaganda about the figure with a good proportion of the aircraft coming from training units; by 1943 front line strength was up to around 1,200 aircraft with 60% being heavies, in April 1945 it was almost 2,400 aircraft, more than half Lancasters, the rest mostly Halifaxes and Mosquitos. In 1943 the USAAF also joined the strategic bombing campaign, flying daylight attacks with the B-17 Flying Fortress and B-24 Liberator while the RAF continued at night; after suffering heavy casualties during early operations the introduction of long-range fighter escorts in the form of the P-47 Thunderbolt and P-51 Mustang allowed daylight operations to continue. Compared to a heavy Luftwaffe attack in 1940 of 500 aircraft with a bomb load of 2,000kg at most, late war Allied attacks simply featured more aircraft carrying more bombs.
I don't mean to harass you but I'm not sure 'inflicting mass civilian casualties' was their primary aim, ostensibly they did it to destroy the industrial capacity of the enemy, although it's true many died in the process. Nonetheless maybe you should to reword your question slightly or some may not deign to answer it :)
edit: I think Dresden and Tokyo are outliers, symbolic attacks that probably weren't representative of the day to day bombing. Things like firebombing Tokyo (the deadliest air raid including nuclear weapons) was probably deliberately intended to kill a lot of people, because the U.S. was willing to be a little more extreme than usual considering the casualty estimates of invading mainland Japan and wanted to force capitulation quickly.
if you are looking specifically at dresden and tokyo (and the other japanese cities), high death rates were a lot to do with the fires the bombings caused, as the bombs dropped tended to be incendiaries. for japan this was very effective because many houses/buildings were made of wood. the resulting fires and firestorm was what really caused many of the deaths. axis bombings e.g. the blitz were mostly just explosive bombs (although they did mix in some incdendiaries, but this was rather limited, and not coincidentally, some of their most deadly attacks coincided with these, like the second great fire of london).
also the blitz was rather limited compared to the latter allied bombing campaigns. comparing a typical blitz attack you might see 500 tons of bombs, with more than 400 being explosive and a bit more than 50 being incendiaries. compare that to the bombing of tokyo, which saw 1700 tons of an epic incendiary cluster bomb that spat out flaming napalm turning the houses of tokyo into flames and fire.
Availability of reliable 4 engined bombers.