There are two misconceptions in this question. Firstly, the RAF did use both the B-17 and B-24. However, they only used the former in the strategic bombing role, and that only for a few raids. The RAF operated the B-17C as the Fortress I, receiving 20 aircraft in the spring of 1941. These aircraft took part in several daylight raids, mainly against German-held ports, but proved to be both unreliable and vulnerable to German aircraft. The remainder were transferred to Coastal Command, which direly needed any aircraft it could get. These were further augmented by a shipment of B-17E (Fortress II) and B-17F (Fortress III) aircraft in August 1942. The B-24, meanwhile, operated as the Liberator I. They were mostly used by Coastal Command, where their great range was vital in closing the mid-Atlantic air gap. However, they were also used by Bomber Command in subsidiary theatres, primarily Burma. Secondly, while night-bombing accuracy was poor in the early war, it improved greatly with time. Improvements in tactics and technology allowed for major increases in accuracy. The formation of the Pathfinder Force (PFF) in August 1942 was key to the improvement in accuracy. This force was to proceed night attacks, dropping markers accurately to give the bomber force targets to hit. The Pathfinder Force was aided by the introduction of radio-navigation aids. These systems, codenamed Oboe, Gee and Gee-H, allowed pathfinder aircraft to be guided accurately to its target by ground stations. The introduction of the H2S navigational radar also allowed aircraft to locate targets precisely at night or in overcast weather. A further improvement to tactics came with the setting up of the 'Master Bomber' system, whereby raids were commanded by an officer in one of the bombers, directing the efforts of the PFF and follow-up aircraft. The introduction of the DeHavilland Mosquito light bomber also aided the PFF, as it could accurately place target markers, or conduct diversionary raids to split the German defences. By the end of the war, accuracy for night bombing was over 90%.

To answer your question, there are two main reasons why Bomber Command didn't use American bombers in Europe. The first is down to the differing philosophies held by Bomber Command leadership and USAAC leadership. The USAAC believed in precision bombing. In this, bombers were to target factories (or similar strategic targets) directly, knocking out targets without damaging the surrounding city. This imposed certain limitations on operations, and hence on the aircraft needed to carry them out. To achieve the required accuracy, the aircraft had to fly in daylight. This meant that they would be exposed to the full force of the German defences, and hence had to carry their own heavy defences. This cut into useful payload - however, this was a worthwhile tradeoff, as what bombs were carried would have a greater effect on the target through the increased precision. USAAC bombers also had no need to carry large bombs, so their bomb bays were short but deep. In comparison, RAF's Bomber Command, under Arthur Harris, believed in area bombing. Area bombing didn't target the factories so much as the cities that contained them. It is difficult to destroy factory equipment with bombs. Instead, Harris believed that it would be more effective to prevent a factory working by destroying the housing used by its workers, forcing them to evacuate the city. Area bombing could be done effectively at night, reducing the risk to the aircraft. This meant that the aircraft used could carry fewer defences, and hence a higher payload. The bombers carried loadouts that were more suitable for destroying large built-up areas. This included large 'high capacity' bombs, such as the 4000lb HC, nicknamed a 'blockbuster' for its ability to destroy city blocks, and large amounts of incendiary bombs. To carry and deploy these effectively, RAF aircraft had long, shallow bomb bays. Over the course of the war, precision bombing proved to be only somewhat effective. While it had proven effective in pre-war exercises, these were under favourable conditions with well-trained crews. When confronted with heavy defences, with poor weather and inexperienced wartime crews, it proved to be somewhat less accurate. However, it was still useful against point targets, such as oil refineries or railway junctions. Area bombing was effective at destroying homes and factories, but much less useful against these targets. This fundamental difference in philosophy had a great effect on aircraft design, with aircraft suitable for one unsuitable for use in the other.

The other consideration was more about the effective use of limited runway space and air routes. Committing Bomber Command to the use of American aircraft would mean committing to daylight raids as well, as these were what the USAAC aircraft were optimised for. This would greatly complicate airspace management over the UK and Germany, as both the USAAC and RAF would be operating raids in the daytime. With Bomber Command sticking to night raids, this issue was avoided. Doing so also allowed round-the-clock raids on German targets. This put a greater pressure on German morale, as they could be bombed at any time. It also meant that it was harder to recover from raids - if a target was struck by RAF bombers on one night, a USAAC raid the next day would catch the initial attempts at rebuilding.

Different purposes and strategic thoughts. Parts of the United States air-force pre-war abhorred the concept of mass bombings against cities (strategic bombing) rather then very limited military oriented bombing (tactical bombing). The B-17 and B-24 were therefore designed not for overwhelming bomb loads, but for targeted bomb loads delivered during daylight (for precision). Therefore they built for greater defensibility, which meant a much larger crew, as opposed to the Lancasters.

Relegating the survivability problem to just flying under cover of darkness or armed escort as the Lancaster did gave a lot of other advantages - in terms of delivering the largest possible load of bombs to a arbitrary place in Europe, Lancaster could deliver massively more bombs, but at significantly greater risk to the crew, even though the crews were theoretically flying at safer times (i,e, night bombing). There is a whole war of words and analysis over survivability rates - but the general outcome appears to be that even given a far more dangerous assignment (daylight bombing) your chance of coming back in a B-17 or B-24 was greater.

The other thing to bear in mind is that the B-17 and B-24s were multi-theater. The B-17 was explicitly designed with long-range in mind - the pacific - not just Europe.

A couple of good resources on the B-17: https://www.amazon.com/Flying-Fortress-Corrected-Edward-Jablonski/dp/1626549044 https://www.amazon.com/Flying-Fortress-Corrected-Edward-Jablonski/dp/1626549044 (by Curtis Lemay) http://ww2podcast.com/ww2-podcast/the-lancaster-bomber/ (A lancaster partisan ;-)