In civil (and criminal) law, yes, but in "förvaltningsrätt", public law, it's somewhat different. Cases are judged mainly from documents and sometimes the state can sort of force you to provide documentation in a manner similar to discovery and subpoena. It's also where you might end up with a reversed burden of proof, notably in tax cases.

It's still a much saner jurisdiction in many respects, especially for physical persons. You might get marginally nicer judgements in commercial law in certain US states, though I'd personally prefer both swedish law and swedish arbitration due to a combination of lower costs and the average quality of commercial law here. The Stockholm Chamber of Commerce arbitration institute is actually rather popular among international corporations for roughly these reasons.