That is a great question, I know when it comes to College Degree choices it can get very confusing. There are many sources of advice online discussing options and outcomes. To be completely honest, it really all depends on what field of work you want to reach.
I have taken Computer Science, Computer Engineering, Aerospace Engineering, IT, Cyber Space, and Software Engineering university courses. They all teach you the different aspect of the technology world. It is good to have a working knowledge of all these fields of study if you plan to work as an engineer for any company. All these degrees have different class requirements and at the end will you will have learned different skills. Most of these degrees start to take shape and separate into their own world after your 2nd year of college.
Different jobs have different requirements, when applying for a job it will show exactly what they are looking for.
If a job entails working with engineering design tools, most likely they will require a BS in the according field.
If you apply for an engineering or software development position, but do not have a BS. Most likely the company will consider candidates who do have degrees.
A degree is a simple form of showcasing that you have meet the requirements for that specific degree. It shows that you have the skills and knowledge to potentially be successful in the position.
There are more factors to consider when applying for a job, but over all for high paying jobs a BS/BA is mostly required, just to show that you are college educated and potentially have the skills needed to succeed.
I hope this helps, if you have any further questions, please let me know.