Synthetics key advantage is time between changes.
Most also resist shearing better than conventional oil, which is important for diesels, Direct injected engines, or anything that produces high oil shear stresses (turbo, direct acting valvetrains, etc.) But that is one of the largest contributors to viscosity break down. Conventional oils usually include additives called viscosity index improvers which help control multi grade oil viscosity across various temperature ranges. These molecules are the ones that suffer from shear stress the most, and this is where synth oil's advantage is clear. Because Synth oil uses synthesized long chain hydrocarbons that help stabilize viscosity and which also happen to be less sensitive to shear stress.
Also, a lot of synth oils include additive packages that can include friction reducers, detergents, or other goodies.