I live in Southfields and had my DD at St George's in 2007 and DS at Kingston 2009.
I decided (begged) to change hospitals because the experience at St George's was so bad. I know a lot of it is down to luck/staffing on the day, and my luck obviously wasn't good, but it was also the hectic, frenzied atmosphere as a whole, and the seeming lack of care from so many of the staff, not to mention the traumatic birth itself.
Kingston, although annoying to get to for antenatal appts (unless you're driving), was a completely different experience. It was calm, friendly, easygoing and helpful. St George's is more like St Mary's in terms of scale, whereas Kingston is small (much of the hospital is only two storeys high). Honestly, it was a fantastic experience all round and I couldn't praise them enough.
I know St George's has a more advanced neonatal unit, which is why I chose it the first time, but I actually felt in much safer hands at Kingston. Somehow the scale made it feel that if something went wrong, the midwives would be able to talk to each other and reach the key staff who mattered. At St George's, on the other hand, something did go wrong and I was left unattended for far too long, staff weren't available and the midwife kept giving me bad/incorrect information (by the end the doctors were sighing/rolling their eyes and correcting her in front of me, which didn't help my confidence).
Oh, and on a practical/comfort level, you almost always get a private room afterwards at Kingston whereas at George's the rooms are shared between four I think, which can be a nightmare. Also, the carpark is almost directly outside the maternity ward at Kingston but quite far at George's.
Good luck whatever you choose!