Hi Ana,
If I were you, I would go to South Kensington 100% (I'm a bit biased because I have my flat in that area). In my opinion, South Ken is a bit more "in the middle" than Camden which is a bit further from the centre. As well, it's a richer area so potentially richer clients. It's a very well connected area (Piccadilly line + district and circle lines). The borough is very nice, you're close to many museums, restaurants, shops, so very pleasant to live there, very good atmosphere.
This is my personal opinion but I also feel safer in South Ken.
I think it really depends on what you're looking for as well in terms of clients and lifestyle, like I think Camden would attract younger clients such as student, musicians, people with alternative styles from different backgrounds when South Ken will get you more older British people (even though I feel that if a client really wants to see you, they would make the effort to travel to you regardless of the area you are in), however I feel that a lot of clients would feel more comfortable going to South Ken than Camden.