OK, I am really not an expert but I have worked in the NHS for years, mainly in maternity care, and I honestly believe that if you want the best medical care you are better off in the NHS. If anything goes hideously wrong in a private hospital you are nearly always shipped off to the NHS anyway. Charlotte's is a specialist obstetric hospital and really knows its stuff, and is right next door to (and part of) Hammersmith Hospital. At the Portland you may take pot luck with the quality of your obstetrician, and they have far less clinical supervision and back-up.
You will get your epidural at Charlotte's. Believe me, their epidural rates are through the roof! A friend of mine who gave birth there joked that they have anaesthetists roaming the corridors begging for work. When I had my epidural, it was done almost instantly and I must say they did it extremely well. When my labour did go tits up and I needed an emergency CS, I was really impressed by the speed and efficiency. And was left with a healthy baby and an amazingly neat scar. All the staff were really lovely and supportive. I honestly can't fault the labour care.
Now, I don't think they're great at everything, and I've heard complaints about aspects of their antenatal care. And I had real complaints about stuff that happened at the Fetal Medicine Centre there. But I would still choose them over the Portland, every time, because I think the midwifery care is of a much higher standard, and the whole system is integrated into a clinical quality system that would give me peace of mind.
I'm aware that I'm pushing you quite strongly in one direction, and that's because I am, frankly, prejudiced against private sector maternity care. I just think that, if something goes wrong, you're better off in the NHS. But if you know of a really good obstetrician at the Portland, and you have real faith in them, then that may be a better way of getting your peace of mind. Just don't assume that because a doctor works at the Portland he's a better doctor. That is just not the case.
I'm sure someone who's had brilliant care at the Portland will come along soon and say everything I've written is rubbish!
Oh, and by the way, whichever place you choose, they're both highly experienced and your birth will be FINE. Good luck!