They center better, provide full torque almost instantly and use full torque to hold a surface in its commanded position. An analog servo needs to deflect a bit to provide full torque so holding power (picture holding a rudder in knife edeg in an aerobatic plane) is much improved.
The downside is they draw more current and cost more.
If you're flying a trainer you may never notice the improvement. If you're flying a high performance plane or helicopter, it will be like a different animal with good digital servos.
http://www.futabarc.com/servos/digitalservos.pdf
edited to correct link