Really...

they didn't account for the weight of the autistic "mathematicians" ego

AutoCAD, SolidWorks etc
Mathematica, Matlab etc

A degree says nothing about your own personal competence, intelligence and knowledge.

I'm in Europe. Many engineers are in math competitions and they win. Some with more theoretical interests go and work on semiconductors/semiconductor physics or control theory for their MSc/PhD studies.
Most really knowledgeable professors (both phyics and eng.) I know easily has knowledge worth 2-3 degrees. Some engineers also have a second degree in applied math; especially control theory or optimization guys.

Real shit begins for both engineers and physicists at MSc/PhD.

If we talk about people who know their shit you can't really compare them because they both know what they need to do their shit. When they don't they learn it. That's pretty much expected at that level.

Anyway a BSc is pretty weak for a comparison in the way you want to do it.
Most of the time you spend there is teaching you the basics: basic math + the basics of your degree's focus.

Essentially the choice is more of a question of interest and talent. Regarding engineers depending on what they do they need to know their physics well though.
No engineer knows everything about engineering and no physicists knows everything about physics.

Yo see and This post has much truth in it. It shows that engineering is more of general problem solving.

>The vast majority of what engineers do isn't physics
True. However regarding the exception:
>Engineering is a *trade*.
Engineering *can* be a trade if you do it like that, but in itself is much broader than that. There are highly theoretical engineering paths you can take for example someone who works on gas sensor physics or on methods for modeling complex systems is really different from the guy who has a workshop and who can build anything. That's not to say the workshop guy doesn't have an excellent in depth understanding of more theoretical topics to assist him.

So I pretty much agree with your post. To add for OP's sake:

An eng. should be able to work at the abstraction level necessary for the problem. For example there are many different transistor models: you need to use the one which fits the problem, you have to have a practical feel for it, knowing the physics makes this possible and a lot easier. Knowledge is needed if you want to improve it or make something new. Depending on what you want to do hat knowledge might be physics.

It's also required of an engineer to be able to understand a process in it's entirety from the underlying physics (at least on a basic level) through various models to the practical device/applications. That's how he or she knows whether something is applicable or how to improve something or even invent something new.

This engineering vs physics vs math is a Veeky Forums meme. Anyone who thinks that university level knowledge in a STEM field is babby tier is retarded. Too bad that half of Veeky Forums believes it which means that they're either below average undergrads or highschoolers or simply insecure as fuck.

TL;DR: NO!

classic school kid who goes to school just to get a job and not because (s)he's really interested about subjects.

Definitely: YES!

What about applied physics/engineering physics?

chemical engineering probably would take a little longer unless you were a chemical physicist