Not really. First, Europeans are bigger than US-ers on volunteering http://www.jhu.edu/~cnp/pdf/table101.pdf
Furthermore, the US data come from the 1996 Independent Sector survey of volunteering and giving that has been criticized on methodological grounds.
According to BLS estimates based on CPS data, http://www.bls.gov/opub/ted/2004/dec/wk2/art05.htm the rate of volunteering in the US is about half that estimated by the Independent Sector Survey. Therefore it is safe to cut the US volunteering data shown in the above table by about half - which puts the US way below Europe. On the top of it, about a third of it is "religious volounteering" - whicj is much lower in Europe (except the UK).
Wojtek