In scenario (A) you will not spend all your day programming. You will have to care about the business parts. If you're not cut out for those parts, even if you end up making lots of money, you will probably not be happy.
In scenario (B) you are more likely to be able to spend more time programming, with less overhead to worry about, but this depends heavily on the employer, so you may end up performing several false starts or walking away from an employer/employee relationship. If an employer accepts you, you will most likely not be paid what your time is worth, but this is a willing exchange for not having to care about the non-technical parts of the story.
Is there a scenario C? If there is I've not yet discovered it.
Time spent finding new clients, for example, is totally unpaid. And most consultants need to spend a fair amount of time doing this.
Ongoing training and education time are also totally unpaid. Clients hire you to solve problems and go away--they won't invest in you like they would an employee.