You are right about the battery life; the 13 Pro Max is near the top of the world in that department, ...huge battery life upgrade.
Now on the cameras; the iPhone 13 Pro Max will make you a better photographer, and videographer. One very important thing to know: You want the 256GB storage model (or higher...512GB or 1TB) because the 128GB model CANNOT use the new Pro Res video mode.
So it is absolutely imperative for the 13 Pro and Pro Max models to not go below 256GB of ROM storage. 128GB is simply not enough for the Pro Res larger files.
And no matter if you are a professional or not it is a feature of the highest end for the very first time ever in Apple iPhone's life history. It's like . . . the Webb telescope they'll send into space in December; it'll see over 15 billion light years in the universe, possibly helping us to know where it all began.
Mike, I think the iPhone 13 Pro and 13 Pro Max (256GB minimum) are the most advanced and performing mobile phones of the entire planet; and not only for battery life and cameras, but almost everything else too. We are getting closer to quasi perfection in the world of mobile communication, the exploration and discovery of the universe, and everything that is inside of it.

...Including the kitchen sink and the high fidelity stereo sound system.