These two books by the same author, on face value, look very different, therefore, let's start out by showing how they contrast. First, Hatchet is fiction and My Life is non-fiction. Hatchet is an adventure story whose primary focus is on one character, Brian, and how he survives a plane crash in the wilderness with little more than a hatchet to help him get by. My Life, focuses on the life of the narrator (also the author), but each chapter focuses on a different dog. These dogs could also be considered main characters. Hatchet is a story of independence and the conflict is mainly man vs. nature. There is very little focus on relationships in this book. My Life, on the other hand, very much focuses on relationships, the narrator's relationship with his dogs. The main conflict is man vs. man.
If you dig a little deeper, you will see that thematically, these books actually have a lot in common. First of all, both books deal very significantly with loneliness. Brian is lonely because he is actually alone. The narrator in My Life is also very lonely, though he is not physically alone. He is arguably neglected by his parents. Because of this, independence and survival are key themes in each story, and as a result, both stories also deal with coming of age in the life of the protagonist.
You could also compare these books by pointing out the similarities of the narrator in each. Because they are both written in the first person point of view, the audience is privy to the inner thoughts, fears, and emotions of the story teller as he experiences them. Many critics have suggested that Hatchet was somewhat autobiographical in that the main character was very similar to the author himself. My Life is a true auto-biography. Certainly, you could look at each main character and compare them directly.
Finally, you could compare the similarities in Paulsen's writing style of each book. He takes a simple and direct approach to each story. They are both written at about a 5th grade level, but the stories themselves are applicable and interesting to adult and child audiences equally. Both books have been hailed as "page turners," and this is due directly to such a story telling style. In each book, Paulsen's descriptions are vivid and life like, but he balances the action of the story so that the reader never gets bored.