I studied both, can't say for sure EE was harder. Some courses in computer science were extremely hard for me (complexity, discrete math) and some courses in EE engineering were equally hard (most of the physics courses, analog circuits and more)

Both degrees can be made super hard, as hard as the school desires them to be...

why would someone pursue a route that's harder AND pays less AND has far fewer jobs available?

And has less cultural cachet.

I disagree. From what I've seen, the lower level you go, the more advanced it is seen by other developers. As the copypasta goes:

At the beginning, there was Purusha. From his face, born was the Brahmin, the priestly caste, the tooling creator, one who develops programming languages, compilers and standard libraries.

From the arms of the Purusha, Kshatriya, the warrior caste, was born. Kshatriya is the developer of systems software; operating systems, database engines, graphics drivers and high performance networked servers.

Then comes the Vaishya, the merchant caste, the Application developer, who was born from the knees of Purusha. From the feet of Purusha, the fourth varnā, Shudrā, the system administrator, was born. Shudrā serves the above three Varnās, his works range from administrating computers in bureaucratic organizations to replying to support requests.

that's by other developers, but I think in the mainstream know nothing culture people have an image of "coding" that's more prestigious and hackery than EE?

I don't know a single person outside the tech bubble who sees "coding" as something prestigious

Well yes, that's why China's in the lead. We willingfully gave it up because corporate decided it was too expensive to pay american talent. They started the death spiral towards "No American wants to work in EE anymore".

Nah I did EE and then CompE (which was just replacing some later EE classes with hardware design stuff) and EE is not "actually really hard" - although people like to put it on a pedastel.

Compared to CompE or Comp Sci?

I never studied the hard sciences very seriously, although I feel like in retrospect I could have done so at much lesser proficiency than someone with much more encouragement, discipline, and interest, so my path of starting with web/software and then diving into electronics and EE would feel quite different

Both?

Hard and well paid gets a flood of people pursing it so difficulty can't be the only explanation. Finance, actuarial science, medicine, and law get plenty of applicants. I think it's that CS is an office job that pays well and is in-demand.