Which Is Faster: Proximal Gradient Descent or Block Coordinate Gradient Descent?

Question

Given a non-smooth convex optimization function which one could solve both with proximal gradient descent and block coordinate descent. I would like to know the difference in scalability and convergence rates between these methods. The objective function that I want to solve is sum of $l(x) + g(x)$ where $l(x)$ is smooth and differentiable, but $g(x)$ is non-smooth and non-differentiable. Moreover, for $g(x)$ I do have analytical solution for proximal operator.