I read that early in the war the British tried daytime bombing but found the casualty rate too high and hence concentrated on less accurate night raids as the war progressed. On the other hand the US was more willing to take losses for "accurate" bombings.
Is this true?
Strategic Bombing was the holy grail of the US Army Air Force during the 1930s. They thought daylight bombing with their large four-engine bombers could destroy critical industries. They developed the Norden Bombsight and thought it could give them the precision necessary to achieve their goal. They also thought their bombers carried enough machine guns to be self-defending. Their most famous bomber in 1940 was even called the Flying Fortress, because it carried 11 fifty caliber machine guns. A later model, the B-17 G carried 13 fifty caliber machine guns. The B-24 was a newer model that was ten percent faster, could carry ten percent more bombs, and had a range that was ten percent greater. However, the B-24 only carried 10 fifty caliber machine guns and was not as structurally strong as the B-17.
Prewar testing showed the Norden bombsight was very accurate. They claimed it could drop a bomb into a pickle barrel from two miles up and had the test data to prove these claims. Yet, these tests were carried out in Arizona and California, where there are rarely any clouds in the sky. They dropped their bombs from 10,000 to 12,000 feet. That is far to low against any target that was defended with anti-aircraft guns. In Europe, the US Army Air Force dropped their bombs from 24,000 to 28,000 feet. Plus, the skies over Germany had far more clouds than the skies over the desert South-west of the United States. In 1943, the German Luftwaffe showed the concept of the Self-Defending Bomber was a cruel hoax. By October of 1943, the loss rate was so high even the US Army Air Force could not sustain them. They stopped daylight bombing, east of the Rhine until February 1944, when they deployed long distance escorts in the form of the P-51, P-47 and P-38 fighter planes. They used drop tanks to extend the range of these fighter planes, allowing them to protect the bombers on deep penetration missions into Germany.
Source: "Winged Victory: The Army Air Forces in World War II" by Geoffrey Perret
You have the basics down correctly. Prewar bombing doctrine (from the Italian Giulio Douhet, the American Billy Mitchell, the British Hugh Trenchard, and the German Walther Wever) asserted that daylight bomber raids by large fleets of heavy bombers would win the next war by forcing the enemy's populace to stop supporting the war effort and it would also destroy vital war making items and factories. The British had a force of heavy four engine bombers, and they did try to use daylight raids. The doctrine said that 'the bomber will always make it through.' High speed, heavy defensive armament, high altitude, and the redundancy of having multiple engines would theoretically ensure that the bombers would make it to their target. Once there, they would be able to chose to either take out any factory they liked or simply bombard the town.
That was the theory. The reality was much more difficult. Daylight raids were incredibly dangerous. Relatively low tech means such as people on the ground with radios could spot enemy raids long before they got to their targets. Higher tech options such as radar could be used for even more warning and accuracy. Cannon-equipped fighters could cripple a bomber in a single pass, and they were faster and could fly higher than the bombers. Defensive armament on a bomber was a good thing, but the difficulties in hitting a moving fighter from your moving bomber were considerable. As such, this method of bomber protection was insufficient. Losses were far too high to be sustainable. So, the British moved to nighttime bombing.
When the Americans entered the war, they continued to cling to their prewar doctrine. Surely the wonder of the B-17 would be able to fly to Berlin, drop accurate bombs due to its Norden bombsight, and make it back home to do it again. And indeed the B-17 was a wonder. It was legendarily rugged and very well armed. It was flown by well-trained crews that were determined to accomplish their mission. And in 1943 these crews were sure they would succeed where the British had failed.
Once again, theory was trumped by reality. The Americans experienced the same unsustainable losses that the British had. For instance, the "Black Friday" raid on Schweinfurt fielded just less than 300 bombers. 60 were destroyed, and more than half of the remaining planes were damaged. Nearly 600 men were killed. After that raid in October of 1943, unescorted raids were suspended.
The eventual solution was applied in 1944. Long range fighters such as the P-51 Mustang were assigned as escorts, and drop tanks full of fuel gave them the ability to escort the bombers all the way to the target and back. Suddenly, bomber losses were not so severe. Also, the Luftwaffe began to be worn down. They had to defend the nation from these raids, but every time they did they were opposed by Allied airmen in fighters that would thin their ranks. Eventually, German fighter opposition dwindled to the point where they were unable to effectively contest the D-Day landings in June of 1944.
So, the US was willing to take losses, but only once they learned that unescorted heavy bombers would suffer unsustainable losses. It wasn't a matter of will alone. The US was willing to undertake daytime bombing and the losses it entailed, but only once they were able to escort their bombers to the target and back. The US did want accuracy in (most of) its bombing in Europe, but even this desire was trumped by unsustainable bomber losses. (I say this to make sure that it is understood that the British didn't have any weakness of will, they merely learned the same lesson earlier in the war)
At the Casablanca conference, January 1943, this very question came up. The Americans, as /u/davratta pointed out, were convinced that daylight precision mass-bombing was the way to destroy the German industrial base. Also as /u/davratta pointed out, the Americans thought their bomber boxes to be invincible to fighters due to the sheer mass of guns on American bombers. The British clucked at the Americans, but weren't able to get it through the skulls of their over-enthused allies that this was a Bad Idea.
The two camps at odds with one another eventually settled on the concept of "round-the-clock bombing" to reconcile their positions, neither of which they were willing to abandon - the British out of experience, and the Americans out of a misguided sense of invincibility.
So, yes and no. The British did indeed find daytime bombing far too costly for their bombers. The Americans, however, weren't making a conscious trade-off - they genuinely thought that daytime raids weren't as dangerous as the British were making them out to be. This same pattern of the British thinking Americans were too eager and unrealistic, and the Americans thinking the British were too cautious and distrustful, continued throughout the entire 1943 conference.
You are correct, the RAF found daylight bombing to be excessive during the first few months of the war, with losses being so high that entire squadrons were essentially destroyed... Part of the reason for this was the RAF were flying medium bombers that were too slow and too poorly armed to survive against the modern German fighters.
In fact, the RAF losses were so high on daylight operations that the only survivor of 8 Squadron RAF was graded LMF (Lack of Moral Fibre) and discharged.
Even later in the war, loss rates averaged between 3-7% per operation with the odd disaster like the raid on Nuremberg which resulted in losses of slightly about 12% due to poor weather conditions for the bombers (contrails at cruising altitude, no clouds and a full moon) but good conditions for the defending night fighters.
The USAAF had very high losses in their early raids over Europe, almost to the point that the 8th Airforce was struggling with morale and fielding bombers for operations. The arrival of long range escorts in theatre in late 1943/early 1944 allowed for a change in strategy by General Spaatz (I think) to destroy the Luftwaffe as a fighting force in the lead up to D-Day (as well as attacking German oil supplies and railways to cripple the German Army).
I should also note that by late 1944, the USAAF had switched to use area bombing as well, with the use of a lead bomber and other bomb-aimers not even using their bomb sights. (I have heard rumours that bomb sights were even removed from some bombers, but I am not sure on the accuracy of this claim).
One of the things that lead the Americans to want to concentrate on daylight bombing that was mentioned but bears more emphasis is the Norden bomb sight.
The daylight bombing raids were started with the idea of doing precision bombing. The Americans predicated their strategy for the campaign around their tests of the effectiveness of the Norden bombsight. In testing and trials the Americans were able to achieve an accuracy of 30 metres. Understandably this lead them to be very optimistic about the possibility of using this bomb sight to destroy Axis industry and infrastructure. Later study found that 16% of bombs dropped with the Norden in combat landed within 300m of their targets.
The British had a slightly different philosophy on the conduct of the war. British senior officers preferred to expend materiel rather than lives to achieve their aims. American commanders were more willing to risk lives, when the there was the possibility of achieving a rapid advantage by doing so. This was a source of friction between the Commonwealth and American forces in North Africa, Normandy and the drive to Germany. Montgomery and Patton personify these tendencies in my opinion.
So the British preferred night time bombing to attrit the Axis, while the Americans wanted to rapidly inflict heavy damage on the Axis with riskier, but potentially much more effective daylight bombing.
Here's a very interesting Talk about the Norden Bomb sight:
