That's a tough one, because I reckon they are both equal with regards to pros and cons. Holland Park is easier to reach from central London, although both are well connected. But Fulham is out of the congestion charging zone, which is a plus for driving clients. I can't see one being better than the other for clients, so maybe think what would suit you best? Holland Park is surrounded by some pretty shady areas, and when I lived there I didn't feel particularly safe walking around at night, whereas Fulham has a more fun vibe, having more shops and bars. For me it'd be close, but I'd opt for Fulham based on thinking I'd be happier living in that area.
I've worked briefly in both of the areas, and didn't notice any difference in amount of work. x
Edit to add: just re read your post title and seen you said 'working apartment', and I've waffled on about living in the areas. Oops, hope it's managed to be of some help