Rest mode, for the most part, appears to download games quicker. It's all anecdotal, but most people will tell you that there is a noticeable difference between download speeds in rest mode versus while the console is on.
This is just something that a good portion of PlayStation users have noticed. This isn't exactly something that Sony advertises like, 'Hey! Put your console in rest mode to download games faster.' It's not a feature in that regard.