Your framing makes it sound like the log is worse in some way, but what the log gives you that the debugger makes you assemble in your head is a timeline of when things happen. Being able to see time is a pretty big benefit for most types of software.

I can always drop an entire state object into the log if I need it, but the only way for a debugger to approximate what a log can give me is for me to step through a bunch of break points and hold the time stream in my head.

The one place where a debugger is straight up better is if I know exactly which unit of code is failing and that unit has complicated logic that is worth stepping through line by line. That's what they were designed for, and they're very useful for that, but it's also not the most common kind of troubleshooting I run into.