The barriers in the public system for psychologists are probably similar. There are bottlenecks in terms of the public system, how referrals have to go. In some institutions you can see a psychologist directly; in other institutions it has to go through medicine.
In the private sector the bottlenecks are created by whether you have the resources to pay for it, whether you require a medical referral to access the service, but generally you can see one more quickly in the private sector.