A traditional stucco system is commonly a little harder and more durable than a synthetic stucco system It will hold up a little better to dings, hail, Woodpeckers, etc. If you live on a golf course, you may have or want to consider a traditional stucco system.
Synthetic stucco is similar to, yet different than a traditional stucco system. Synthetic stucco is commonly applied over a foam insulation board, a form of mesh (either metal or fiber) and applied in two coats.
Synthetic stucco is available in many, if not most, paint brand colors and the color is throughout the material. This prevents it from yellowing or fading, requiring repainting over time. Also, synthetic stucco systems are more flexible than a traditional stucco system. This helps in preventing cracks that are almost inevitable in a traditional stucco system.
Additionally, by being more flexible, synthetic stucco is better for applying over ornate details, accents, cornerstones, etc. It also allows for a smoother finish, if desired, and created much tighter and straighter corners.