One of the most persuasive reasons to push logic out to the database is to minimise traffic. In the example given, there is little gain, since you are fetching the same amount of data whether the logic is in the query or in your app.
If you want to fetch only users with a first name of Michael, then it makes more sense to implement the logic on the server. Actually, in this simple example, it doesn't make much difference, since you could specify users who's lastname is Baldwin. But consider a more interesting problem, whereby you give each user a "popularity" score based on how common their first and last names are, and you want to fetch the 10 most "popular" users. Calculating "popularity" in the app would mean that you have to fetch every single user before ranking, sorting and choosing them locally. Calculating it on the server means you can fetch just 10 rows across the wire.
