The documentation answers this:
The .NET Framework 4 Client Profile is a subset of the .NET Framework
4 that is optimized for client applications. It provides functionality
for most client applications, including Windows Presentation
Foundation (WPF), Windows Forms, Windows Communication Foundation
(WCF), and ClickOnce features. This enables faster deployment and a
smaller install package for applications that target the .NET
Framework 4 Client Profile.
A smaller install package could be a bonus, especially if you're targeting non-traditional devices like tablets with less storage space. It's also a shorter download time if the Framework needs to be installed.