I've only read four chapters, but Toshokan Sensou: Love and War Bessatsu Hen appears to be essentially a very long fan-pleasing epilogue to the original manga, Toshokan Sensou: Love and War. If you really loved the original, but at the same time wished you got to see Atsushi and Iku actually dating, well, you got your wish, and so far, I'm definitely not disappointed. Nothing is left out, as it starts right where the original ended, but before its epilogue/time skip, that is, Doujou is still in the hospital from being shot in the leg when this manga starts. If you came upon thismanga without having read the original first, then go read the original, because this one will not make any sense to you without having read it first.