MathSciNet is the online version of what used to be the Mathematical Reviews. It contains not just the bibliographic metadata of the paper (in a variety of useful formats) and a link to the actual article (if it exists), but also a review of the article. The reviews are perhaps the single most important feature of MathSciNet.
Google Scholar contains the link to the actual article (if it exists) and the metadata can perhaps be extracted automatically -- for example, Papers (a Mac OS X application) does just that -- but it does not contain the review. Apart from the lack of the review, the main disadvantage of Google Scholar, which probably will become less of an issue asymptotically, is that many entries contain errors in the metadata.
Personally I always check MathSciNet first and Google Scholar second, if at all.
As mentioned in the comments to the question, MathSciNet only contains published work, whereas Google Scholar will list anything which has a direct or indirect (i.e., as citation) web presence. However (at least in my field) it is enough to check the arXiv for (pr)eprints.