The UK and US have fairly substantial differences in their underlying educational philosophies. In my field, in the US Masters degree programs are generally one or two years long and include both course work and research in equal proportions. In the UK, Masters degree programs are a year long and have little to no research requirements. As for the level that the taught components of the programs are taught at, they are pretty similar across the two countries using similar textbooks and covering similar amounts of material in terms of both breadth and depth. The US and UK institutions I worked for accepted students from both countries and while international students often have more difficulties than home students, it is not obvious to me that going UK-US or US-UK is easier.
As for the difference between a US and a UK Bachelors degree. Final year classes taught in both countries again use similar textbooks and cover similar amounts of material in terms of both breadth and depth. In my experience, there does not seem to be a substantial difference between students coming out of US and UK institutions in regards to their preparation for graduate school. That said, there are substantial differences in these students. The US system provides much more breadth of education (e.g., foreign language requirements and general education requirements) that are absent from UK universities. I have never heard an admissions committee member in the sciences argue that student X is is more likely to succeed than student Y because student X is competent in a foreign language.