What are the main differences between Graduate school in the UK vs US?
I don't think your measure of 'easiness' is really correct. Finding a supervisor isn't a measure of how strong a student you are, it's a measure of how the course works and so in what circumstances a supervisor will take you on. 

You haven't said what you mean by 'graduate school' in North America. Usually you would compare doctoral programmes, and there you'll find the UK 'harder' on average, because a US programme begins with taught courses that don't form part of the UK programme (as much).

A taught MSc in the UK is only just above undergraduate. You essentially do a typical undergraduate year of taught courses (which may be very very similar to ones taken by undergraduates) and then spend the summer doing a 3 month research project. You therefore don't need to start with a supervisor, as you have 8 months to find one, and you will always be allocated someone. Just below this are a selection of 'undergraduate masters' courses, where undergraduates study for a fourth year, beyond the normal degree programme. They basically do the same as the MSc except for missing the final project (or doing one instead of one of the taught modules).

If you looked at an MSc by research, I doubt you could get on to that without a supervisor. That is closer to doctoral study. Slightly up from that is an MPhil, which is roughly the first part of a PhD, and actually is in some subjects.