I haven’t seen any evidence that “most people at Quora says that a CE majors can do any thing CS majors do.” The claim is simply false.
Computer science and computer engineering are different fields. Yes, they heavily overlap, but they focus on different components of the computing pipeline. As a general rule, computer engineering is more focused on hardware (and its underlying principles, like electromagnetics, signal processing, and control theory), while computer science is more focused on the software (and its underlying principles, like algorithm design, complexity theory, and formal verification). Computer science is also more likely to cover subfields like human-computer interaction, computational biology, and computational linguistics.
It may very well be true that a goodcomputer engineering curriculum can cover all the material in, and convey the same set of skills as, a mediocrecomputer science curriculum, but that sentence remains true if you swap “science” and “engineering” in the field names. Sure, both computer scientists and computer engineers can write code, but that’s like arguing that both philosophers and historians can write prose.
At my university, computer science majors are in (slightly) higher demand by employers, and they receive (slightly) higher starting salaries, than computer engineering majors. Make of that what you will.
td;dr: The advantage of going for a CS degree is that you get to study more CS. Symmetrically, the advantage of a CE degree is that you get to study more CE. Which of those is actually an advantage depends on your interests, your experience, your goals, and the quality of instruction in the two majors at your university.