How does each of the US military branches basic training compare to each other?
In terms of physical difficulty, it goes Air Force -> Navy -> Army -> Marine Corps.
Other than that, each is tailored to the skill set needed for that branch.
All of them are designed to grind up a group of individual civilians, mash them into pulp, and form that pulp into a unit comprised of military servicemembers. The point of basic training is not for you to succeed. In fact, you will not succeed. Your unit will succeed, or fail, together. And that is the point. Individuals do not graduate from boot camp - units do. And the longer it takes you to figure this out and to stop being an individual, the harder boot camp will be for you.
In boot, when a member of your unit fails, you fail too, even if you did nothing wrong and everything right, even if there was nothing (or nothing more) you could or should have done to help that person - because that's how it is in war. And war is what military training exists to prepare you for.
No matter which branch you join, it will be about a me-into-we evolution, accompanied by instruction in certain skills, and the development of a military mindset and work-ethic.
So, to answer your question succinctly, boot camps are more similar than they are different - the main evolution of all of them is the same, but the skillset each one teaches and the attributes required by each service differ based on the needs and the mission of that service.