I agree about being able to see the whole program execution. This is particularly useful for multithreaded code since it provides a linear view into how the program actually executed. How are you supposed to figure out that A happened before B in a multithreaded program using only a debugger? With adequate logging, even if you don't log the precise times for A and B, you can often infer the ordering of these events based on other logged data.

For a lot of glue type code, I don't actually care about stepping through something line by line. I really want to see how components interact, not each step of execution. Though I do wish languages had better support for doing something like printing out all local variables in the current function along with the stack trace, sort of like a very shallow, low-cost dump.

Another big advantage is that logging is usually much easier to turn on (or even keep on by default) for production scenarios. Good luck getting some bank to let you run a debugger or even get a dump for anything.