Althrough different in genres, they both share one major thing - the animation style. They are both animated to look like manga, but with moving pictures. While Yodaka no Hoshi is more drama, Tengen Toppa Gurren Lagann Movie: Lagann-hen Special - Viral no Amai Yume is more comedy. But if you enjoy not so common animation styles, you´ll surely like both.
There are lot similarities between those two. There is animation style which looks like manga. Both are videos from genres slice of life and drama with some supernatural effects, fantasy parts. In both you can see flashbacks of main characters life. Apparently both videos have really nice music, so even if style of animation or story isn't in your taste then you might like music which in both videos is really good. There are more common features which you can easily notice watching "Yodaka no Hoshi" or "3-gatsu no Lion meets Bump of Chicken".