It's true that the Lancaster typically carried more offensive load than its U.S. contemporaries, but on the other hand it had vastly lighter defensive armament, fewer crew members, less armor, and a much lower service ceiling. A B-17 could carry similar weights if you stripped out most the guns and armor and flew them at 10K feet lower than their usual altitudes. This does not mean one airplane was better than the other so much as that they were employed differently.
Twin engine aircraft could carry similar loads at times (not just the Mosquito, but also models like the Wellington or the Marauder) but typically either over less distance, at lower altitude, or with less protection. The Mosquito bomber variants had no defensive protection at all aside from speed.
The B-24 had a larger bomb bay than the B-17 and hence could carry a larger volume of low-density payload. The Liberator was also structurally weaker than the B-17 and more vulnerable to battle damage. In general being a crewman in a U.S. heavy bomber in Europe was statistically just about the worst job in the war, better than being a U-boat crewman but worse than about anything else. The attrition was horrible. U.S. propaganda tends to avoid discussing it, but by late 1943 the U.S. strategic bombing campaign was effectively defeated and had to be suspended (bad weather was listed as the official reason) until a sufficient quantity of long-range escort fighters came available.
The B-29 was a somewhat immature design that didn't become fully developed until the advent of the B-50. By American standards the B-29 was relatively vulnerable and particularly prone to catching on fire. It did okay against the Japanese (who wholly lacked fighters that were effective at 30K-plus) but it's just as well the U.S. didn't deploy them to Europe.
