I'm afraid I haven't read all the other replies, so apologies if the gist of this is wrong.
I emigrated to Australia a year ago. Previous to this, I'd sought treatment/diagnosis on the NHS for a variety of things, including ADHD, interstitial cystitis, joint problems etc with little or no success. If I was lucky to get through the GP stage, I would fail or be fobbed off further down the line.
Since I arrived in Australia (and I am on reciprocal medicare here, not private) I have had successful diagnosis and treatment of ADHD, depression/anxiety, chronic tendonosis (following on from pregnancy) and hypothyroidism.
My GP over here couldn't believe that having recurrent intrusive fears of putting my baby in the microwave when mentioned to the HV weren't picked up as anxiety related to PND, and that I wasn't routinely tested for thyroid levels when I went to the GP in the UK about fatigue (falling asleep uncontrollably almost every day), or even questioned about other things (such as feeling the cold, dry skin/hair and weight gain) which would have instantly rung alarm bells.
In addition, I don't have a lecture / patronising talk when I need a repeat for low-dose, taken when needed oxazepam for panic attacks. The prescription is given to me with a smile and encouragement that hopefully the other treatments will start to take effect soon, and if anxiety is a lesser impact in my life, then I can work on getting better, easier. I know my friend in the UK who had similar issues wasn't treated anything like as compassionately.
I have a problem with my pelvis at the moment. It's a chronic ongoing thing since I had DD (nearly 3 years ago) that has got worse since I've started running. In the UK I had an ultrasound scan (that took 3 months to be referred for), nothing was found, so I was put on long-term pain killers and told to stretch more. In Australia, I first went to the doctors about it a month ago. I've had 5 sessions of private physiotherapy since then. I went back today saying that I was still in considerable pain, and the physio thought I had severe tendonitis and tendonosis. I was referred for a cortisone injection for the pain, and to relax the muscles. I'm having this on Friday, but only because I wasn't able to make the appointment tomorrow. This is fully paid for by medicare.
There are differences that are due to the way the Australian system is funded compared to the UK system. For example, I'm trying a new anti-depressant. It's new, doesn't have much of a track record, and works in a totally different way to normal ADs. It's also much more expensive than your sertralines and citaloprams. I know this drug isn't available on the NHS, so I would never be able to try it in the UK. It might not even work, but at least I can have the choice to try it.
The way counselling works as well is different - I have to pay part of the fee (about 15 pounds for a 45 minute session) but I was able to access this within a week.
Individually, you will always get good healthcare providers and bad ones, one of the GPs I've seen in Australia was shocking (I was told to try meditation when I was bouncing off the walls and cutting myself every other day) and one of my GPs back in the UK was great. However, it seems like the quality of care in Australia is supported, rather than held back by the public AND private provision in healthcare. Australian hospitals are either private, or public, not the pseudo public PFI that you get in the UK, and I think this helps to reduce some of the beaureaucracy and red tape.
From the Guardian:
For example, while the capital cost of rebuilding Calderdale Royal Hospital in Yorkshire is £64.6m, the PFI scheme will end up costing Calderdale and Huddersfield NHS Foundation Trust a total of £773.2m. Similarly, the cost of building the new Walsgrave district general hospital in Coventry will jump from an initial £379m to an eventual £4bn.
Also funding is allocated per person rather than per area, so you can apply for a certain amount of allocation for things like counselling, physiotherapy etc, after which you have to re-apply to see if you still qualify for subsidised treatment. And this is qualified for by a need basis rather than means tested.
That's my 2p on the matter. Or 2c as is it in Australia :)