Is it normal for adverts for US jobs to give much less information than European ones? At the moment I'm looking for my next position (most likely postdoc level, potentially one step up from there). 

When looking at advertised positions in Europe I generally expect to see a brief summary of what the job is about on the advert, and then have the ability to click through to see one or more multipage documents detailing the responsibilities of the post, the exact qualifications that are required and desirable, and so forth. Typically these detailed specifications will be used in the selection process - and so an applicant will use them to inform their application, making sure to address each point.

When looking at a couple of positions in the US, there has been the initial brief summary... and then nothing else. The entire job advert seems to consist of one paragraph giving an overview, plus some boilerplate about equal opportunities.

Is this normal? If so, what are the reasons? Since the selection criteria aren't being disclosed, how can an applicant go about identifying what attributes they need to highlight in their application?
In Europe, at least in science, a postdoc is generally hired with specific funding to undertake a specific project. This might not be the case in the US, where lab heads will take on postdocs with a general idea of the area they will work in, but then it will be up to the postdoc to design their own research program. 

Also note that the law around employment in the US is much less restrictive, so where in Europe an employee can call foul if asked to do something not in their job description, and an employer can only sack an employee if they prove to be below a what would reasonably be expected on a listed responsibility on their job description, these things don't apply in the US.