I've had NHS ones since November. I have high frequency hearing loss (typical old age), which means I don't distinguish many consonants from each other, hence lose clarity in speech. The aids have made an enormous difference to conversation, hearing lectures, hearing others at meetings etc. "Cocktail parties" and noisy restaurants/pubs are still a problem but better than before. As for comfort, normally they are perfectly OK, but occasionally get itching.
Mine are the new Starkey Kinnect type, made for control by iPhone (or Android I think). This is very useful. You can adjust settings or switch them on/off from the phone or an Apple Watch. I find this useful, because the one thing they are crap at is listening to live music. Though the audiologists swear blind that they have switched off all frequency shifting, there is a frequency shift between notes heard directly (or through bone conduction when I am playing the clarinet) and those heard through the aids. About a quarter to half of a semitone, which is enough to drive me mad. So I switch them off for playing or listening to live music. I need to do this quickly if I am in, say, a rehearsal, so that I can hear what other players are saying when we are discussing. The Apple Watch does this very well. Fortunately I can hear the entire range of orchestral instruments (not all the overtones though) so I don't need them for playing. It's the high speech frequencies that are problematic.
There are some real advantages. In effect you are walking around with a pair of high quality Bluetooth earphones. Music heard only through the aids is fine, and calls to the iPhone go straight to your ears, which is great.
Before getting them I had a long discussion with a friend who is a senior audiologist. She said the NHS ones are just as good as the private ones, but the private audiologists may take more trouble in setting them up. Her advice was to be demanding and insist that your issues are understood. As mentioned, all the consultations are covered by the NHS, and I've been back three times to get adjustments made.
The only reason I can see for private is if you want aids that are concealed entirely inside your ears (which wouldn't have suited my kind of deafness anyway, as this would occlude low frequencies, which I hear well). Or ones with rechargeable batteries. But battery supply is free anyway.
Hope this helps a bit.