Hi Brandon,
The modeled Bevel uses more Vertices, but looks better, the Shader version is faking the roundness of Edges, a bit like Shade Smooth:

The sihouette doesn’t change, when using the Shader Bevel.
There are situations, where modeled Beveling becomes quite a challenge and, if you’re not getting too close to the model, using the Shader Bevel might save you some headaches (simple example):
