The stressful period for most doctors is getting into medical school, getting through medical school, and getting into and through internships and residencies. That is roughly 10 years or so, and during that time it is absolutely at the pace and pressure I see in software development..but once they finish, for most of them, it is pretty smooth sailing. Those at the top of the game are a different story, but that's true anywhere.
The real difference is that doctors have a powerful lobby that artificially limits their numbers, essentially providing a benefit similar to unionization. You can't massively up the numbers of doctors being trained in the U.S., and you can't import massive numbers of foreign workers to increase supply. No matter how many capable people there are, the numbers will remain artificially constrained.
Software development doesn't have this protection. The only lobby in software development is regularly pushing for massive increases in supply through various channels. Doctors' salaries have continued to rise year after year..not so sure software development salaries will fare as well in the coming years..especially after we convince software devs they are already overpaid ;)