Hi The NHS provide hearing aids on loan so there is no cost involved, that's obviously good! I guess the negatives with the NHS are in some areas waiting times for appointments, that's initially to start the ball rolling, fittings and ongoing aftercare adjustments etc, can be quite protracted, but not in all areas.
The technology supplied by the NHS has improved tremendously over the years but by the very nature of NHS procurement tends to lag a little behind what is available privately.
The BTE (behind the ear) hearing aids provided by the NHS are not to everybody's taste but there again they are quite a bit smaller than previously supplied.
If I put it like this - NHS = free on loan :-)
Private - Faster delivery and (in theory) more attentive aftercare, latest technolgy, better cosmetics :-)
Regarding cost, you'll find each manufacturer has price points at which they will supply a level of technology, an example would be certainly on the internet in the UK you would pay around £1495 or £1595 GBP per ear for top of the range technology and less as you go down the range.
Whether the NHS offering is good for your high frequency loss depends on what they are supplying and how skilled the person is that is adjusting your hearing aids. The end result in the main is dependent on the technology used and how well it is set up.