Differences between the American Lexion and the "European" one: (Cat distributes the Claas combines in the USA): It takes more power to operate in the high yields and moisture often associated with European crops, especially when chopping and spreading.
A Euro Lexion 570 has roughly the same power as a Cat Lexion 580R. Or, a 9880 STS vs. a 9860 STS, they are virtually identical, but the 9880 has nealy 100hp more (mainly for the chopper, but conditions as well). North American corn and rice crops are extremely high volume and require large grain handling systems.
For example, the Cat Lexion 580R has a much larger clean grain elevator and the high performance JetStream cleaning system vs. the 580 used in Europe. When harvesting 180 bpa wheat at or above 18% with the header only a couple inches from the ground, the chopper's better be capable of spreading full header width, at least up to 30' evenly.
Undercarriage restrictions, gross machinery width (with axle and wheels) has to abide by strict Euro width restrictions which limits the flexibility of tire use. Duals and Single tires over 35 inches are prohibited during transport so most end up using 800 (30.5's) or smaller. Headers, for the conditions, a huge head in Europe is a 30' platform.