I had 2 DCs at the Portland and was v happy with it. I can't compare it to an NHS experience so none of the following is intended to imply that it is "better".
It wasn't particularly "luxurious" (I'd say pretty much like a travelodge) although I've heard rumours of suites (I'm sure Victoria Beckham had at least the Travelodge Plus option!) It was spotlessly and scrupulously clean, and the staff were lovely. Not rushed, took time to show you things (they took DH aside to give him a lesson in how to bath ds, which was very sweet), etc - bar none, they were kind and helpful. The food was tasty and there was good choice. If DH wanted to eat with me, I just ticked an extra box and another meal was brought. Interestingly I can remember that I had to pay for extra meals separately and it was definitely not expensive. I could order tea and biscuits any time I wanted, which was really nice when visitors came, not so much my mates who would ring me and ask if I wanted a cappuccino bringing in, but grandparents who had come up on the train etc. Visitors could pretty much come whenever I wanted.
Medical side was impeccable. My FIL was a retd consultant who had worked in the gynae dept of several London NHS hospitals and he had no criticisms (and I think he was predisposed to have some!). He knew either directly or indirectly several of the consultants and had nothing bad to say (and Drs do like a good bitch!)
DCs could go to the nursery at night but it wasn't like they were whisked away or it was obligatory. I think I tried once (was shattered) and they brought ds back and said he was unsettled and needed his mum. Completely right.
There is a lot of emergency/neonatal support if needed (I didn't). That was a rumour that wasn't true when I went there and that was 15 years ago pretty much. Dunno if people may transfer over at some stage due to cost, but the resource is there. The sad incident with the mother who died happened before I went there, so maybe 16 or so years ago. I'm not minimising it in any way, it sounded terrible, but it was a long time ago.
I have very fond memories of my birth experience there and always am slightly amused when it is depicted as the Ritz with a delivery room round the back. It's PR is a bit skewed, I think.