macpherson strut has a single wishbone (usually, the rens do, vauxhalls and fords use tie bars etc), and as the suspension is compressed the camber angle changes.
Double retain the same camber angle through the suspension travel.
The main benifits of double wishbones over struts are they are usually easier to fine tune. Its much easier to build a fully adjustable double wish than a macpherson set up.
Basically more of the tyre is kept in contact with the road through the suspension travel.
However the double wishbone set up takes up more room and has more things to wear and dearer to manufacture.