I retired from audiology in 2021. I have fitted hearing aids to service personnel, private patients and worked for the NHS.
The advantages of private aids, short waiting time, if you pay for the very expensive aids you may get the latest technology.
Advantages of NHS, you have already paid for it, same technology as mid range private aids that can cost thousands, lifetime backup/ support.
Most people wait years too long to get there hearing tested, but if you are in a hurry go private.
If money is no object go private.
Top tip, it is not just your ears that degrade with age, the brain is really where we process the information from the ears and make sense of it. The processing power available to make sense of that information gets less as we get older. Suddenly giving our older brain more information to work on won’t give instant results, it takes time and practice so you have to wear the aids and give your brain time to get used to the new situation.
If you go to the NHS, be nice to the audiologists, they work hard and are under paid:-)