The "piece of paper", whether it is a "diploma" or a "degree" is, IMHO, far less important than the opportunity to learn the skills, techniques, and information that will provide a foundation for your future in the culinary field.
Regardless of how you learn the fundamentals, i.e. culinary school, apprenticeship, or O.J.T., you should plan on spending 10-15 years gaining work experience before you achieve the "rank" of chef. It may come sooner but you need to plan all the same.
What do YOU see as your career path and career goal(s)?
Once you define YOUR path and goal(s), the choice should be much easier to make.