Regarding Diebuster, there are generally two kinds of people. Those who hate it and think that it ruined the world that Gunbuster created and those who think it needs to be viewed as something within the Gunbuster world but seperate to the original series and enjoyed it. I tend to fall into the latter group. While not perfect by any stretch of the imagination and not quite as compelling as Gunbuster, Diebuster does have a certain spark and life to it that few anime manage. The classic 80s style is replaced by something that looks a bit more mid 00s and the world of space monsters becomes much less focused on grand battle outside of this galaxy while traveling at lightspeed and more focused on simple fights within the solar system. Overall, it's a good show with a fantastic ending that calls upon just the right amount of throwbacks to Gunbuster without spoiling it's own story.
Nono is a girl with a dream of being a Buster pilot, however she lacks the psychic ability needed to pilot the newfangled Buster machines. Can she make it to the top? Can she find a way to beat the odds, become a Giant Robot pilot and save the solar system?