IME if I had to guess how well someone would work out and was told only the degree, I would answer:
physics/math degree > EE/ME degree > CS degree > humanities degree.
This is because in my experience, CS degrees are incredibly popular and a lot of people get them even though they may not be particularly good at programming or even enjoy it. 20 years ago, I'd put the CS degree higher up, but today Universities have lowered standards significantly and are minting lots of CS graduates with dollar signs in their eyes.
But that's not how it works because those with only a college degree are (for the most part) not competing for the same set of jobs as those with work experience. They are competing for internships, and when it comes to internships, you are going to hire someone with a CS degree over someone with an EE degree. Therefore you are right, when it comes to internships.
When someone has only a degree and no work experience, that's a risky proposition -- those candidates should be routed to internships so both sides can get to know each other without a long term commitment. In all the companies I've ever worked with, we've never hired straight from college without it being an internship. More likely than not, an internship will result in a job offer if it goes well, and IME most do go well. That means that in practice, it's much easier for college graduates to enter the labor market. But they enter via internships that are converted to offers and generate work experience. Then the work experience is all that counts and the degree becomes a checkbox.
In other words, your college degree is important, but it's important to open the door to your first real job by getting you an internship. After that, it very rapidly decays in importance. This is because the work experience is so much more informative and relevant than the education. I've never looked at anyone's grades or honors, and it's not uncommon to have a lot of employees without a college degree if they have proven their skills in other ways. This disregard for grades or degree and focus on actual skills is what makes things like dev bootcamps work (for good or ill).
In contrast when you screen resumes you invariably come across people who apparently managed to get a CS degree without learning anything. They won’t be dissuaded from applying to technical positions but if one doesn’t have a CS or related technical degree they probably have some confidence in their own ability.
There’s also a factor where some employers simply pass on resumes if the candidate does not meet strict degree requirements. This also increases the average quality of the non-CS degree holder a bit.
Call me cynical, but if I were to see an art history major switch to programming, I wouldn't think "this is a person that decided he loves CS more than art history", I'd think "this is a person that loves art history and ran out of money."
Of course that's all from the resume. Once you actually meet someone and work with them, you can find out pretty quickly how passionate they are and where their interests are. But we are talking about making judgements off of resumes, which again is why work history trumps all. If someone succeeded at a place with similar requirements to yours, that is a much more important signal of qualification than education, so once you land that first job, whether you were an art history major or cs major isn't so important. Might as well study what you love and then figure out how you fit into the labor market later.
What I implied is that people tend to look for jobs related to their degree if they don't have a good idea what they want. There are those passionate CS degree holders and dispassionate CS degree holders applying for a (say) software dev job. There are probably very few dispassionate humanities degree holders applying to the same job. It's some signal, and I don't think one has to dismiss the importance of a CS degree to see that.
In addition I’ve heard of an seen a number of things in CS programs to make me question their quality. I can’t speak to the other degrees.
This is mostly in the Asia/Pacific region though, it might be different elsewhere.
Edit: it's also worth noting as an ex-hedgie that in technical roles most of the firms specifically filter for people with musical ability for this reason.
Computer science degree holders were mostly lacking ability in my experience.
But I wouldn't count anyone out by their degree.
But I agree with you.
I’ve also worked with some really smart people from a physics background.
Similar kinds of problems come up in physics, so for me this tracks.
Surely though a B. Eng. Software with first class honors is better than a random science degree.. ?