The difference from the statutory fund lies in the detail. People with statutory health insurance also have free choice of doctor under § 76 SGB V, but only among doctors with a statutory health insurance license. Privately insured people choose from all licensed doctors in private practice, including purely private practices. On top of this comes direct access to specialists without a referral and without thinking in quarters.
Private health insurance is also more generous when it comes to choosing a hospital. The statutory fund refers you to the nearest suitable hospital and passes extra costs on to the patient if you choose another one. Most private plans, by contrast, reimburse treatment in the hospital you choose freely. There are limits for mixed facilities, for example clinics with a health resort character. We recommend that you get written approval from the insurer before stays in such facilities.