One way that it would be different is that we wouldn't get to see such an endearing, kind and loving side of Liesel's foster father, Hans. Every single night he wakes himself from slumber to go and comfort Liesel; not only this, but he stays up late with her, for hours, talking to her, comforting her, and teaching her how to read. We already know that Hans is kind, but Liesel's nightmares show just how wonderful a man he is. This endears us to his character, makes us more emotionally invested in him and in the story itself, making for a more poignant novel overall.
Another way that the novel would be different is that it would have been a lot more light-hearted. The novel isn't inherently light-hearted at all, but, Liesel's nightmares keep her struggles and suffering front and center, and reminds us of the devastating war. Her nightmares are also a way for Liesel and Max to bond; they both connect initially over having nightmares. It brings them closer together; without that bond, they might not have grown as close. The nightmares also provide a symbolic healing, as near the end of the book, she overcomes them. It gives us a sense of her maturity, and that hardships can be overcome.
I hope that those thoughts helped a bit; good luck!