Some interesting stuff here, including links to more studies showing similar results in different countries.
The summary is that the reason motorists break more laws is that speeding is so common.
I don’t think this is because motorists are all evil and cyclists are all saints. Probably, the reason motorists break speed limits is that it can be relatively difficult to keep cars below the speed limit. It’s all too easy to absentmindedly speed up. It’s also, perhaps becuase of this, widely seen as socially acceptable to break the speed limit (speaking anecdotally).
One interesting thing here, which may not surprise regular readers of Fuck Cars, is that better cycling infrastructure leads to less lawbreaking by cyclists. As is often the case, it’s the design of roads and cities that changes behaviour, not abstract appeals to road users to be sensible!