Hi Lizzie,
I had my baby at St T a year ago. At my first real midwife appt I asked about Home from Home vs Birth Centre and she basically said -- don't worry about that for now. They don't really get into that until the 3rd trimester, because so many things can happen between now and then to influence the decision.
I had been thinking home birth, or possibly Home from Home, but around 34 weeks they found out I was carrying an enormous baby, and so my midwife (who was very pro-home birth, all the St T midwives are) said I had to go into the Birth Centre. This is because of the risk of the baby's shoulders getting stuck, in which case they need a lot of people on hand very quickly.
My overall experience with St T was a bit mixed. I found the antenatal care pretty good (not the classes though), but then the last month was quite awful as I had a number of appointments with midwives and doctors and they all kept telling me different things about how delivery would be handled, which made me very nervous.
The Birth Centre isn't really so much different I think, you can still use the garden room, the rooms are just bigger and with more stuff in them.
The postnatal ward is really not bad at all, I thought, and the follow-up visits at home were fine.
I think the main problem with St T is just that it's so busy. There was a lot of miscommunication during my last month and even during delivery that just seemed unnecessary and in the end could even have caused problems, so I think it's good to be sort of assertive and make sure your partner knows everything you know and can speak up for you during delivery.
But it is one of the best hospitals in the country so don't worry! You will be in good hands 