Amalgam (silver) fillings last considerably longer than composite (white) fillings. Amalgam fillings can last 30 or more years whereas composite fillings usually need to be redone approximately every 10-20 years.
Composite fillings are done primarily for two reasons:
1. Esthetics
2. They mechanically bond to tooth structure so the cavity preparation can often be more conservative (smaller).
Composite fillings are extremely technique sensitive, meaning that the dentist must keep the area completely dry, if even a little moisture gets on the filling it will severely compromise the longevity.
In summary, in most cases amalgam (silver) would be the preferred restorative material as they are stronger and last longer and are recommended for people who have high cavity risk.
From what you are telling us it seems like silver fillings would be a good option for you, maybe try to find out more specifically why your dentist recommends white fillings in your case.