When you hire an independent cleaner, you are the one in charge. But if the cleaner is sick or otherwise unavailable, you’ll be left without cleaning help. In addition, you are considered the employer. Unless you yourself pay their insurance (liability and workers comp), you will not be covered in case of damage, accident, or theft.
When you hire a cleaning service, you will be a customer, avoiding the headache of being an employer. However, you may have less flexibility in certain matters, such as which cleaning products are used in your home. And unless you request otherwise, the service could send you a different employee every time.