Synthetic:
Better cold-flow performance
Better resistance to coking at high temperatures (sludge formation)
Higher film strength to better protect when thinned by high temperatures (a 5w40 synthetic performs comparably to a 15w40 conventional)
Fewer viscosity improvers required so it holds it's viscosity better under shear stress (gearbox and clutch).
But even synthetics are not created equal... here's a comparison of one conventional, one blend, and several other full synthetics... note the viscosity at the end of the run. These samples were all taken from my Vulcan 1600:
http://personal.linkline.com/rlockyer/oil/oil.xls
Castrol GTX did as well as some of the synthetics!