In either case, you had better check the consultant's need for control because that varies among generalists and specialists alike. What you want, of course, is a good match between your need for control and the consultant's tolerance for it. When considering the use of a consultant, it is important to know if you require the services of a generalist or a specialist. You might require both. Generalists are usually better at helping you define the problem.
Specialists tend to frame the problem to fit their solutions.
Either can be of help once the problem has been defined. Neither will be of much help if their need for control is at odds with yours. Choose your consultant with care, and give thought to the difference between a generalist and a specialist.