One advantage for me of MathSciNet is that Google Scholar doesn't give me easy access to the full text of an article, even if my university has online access to the full text of the journal, whereas, if I use MathSciNet (I can get access at home via the university library), the library somehow gives me a button linking back to the card catalog entry for the relevant issue of the journal, which will get me the full text in a few clicks.
Now, this advantage is perhaps peculiar to my university. When I was an undergrad, the library had a proxy, which would prompt you to log in to access something like ScienceDirect, so you'd get prompted for a password clicking on a link from Google Scholar and then have access to the full text. But, as it stands, if someone tells me to go track down a specific article, MathSciNet is probably the easiest way for me to do it.
