With the availability of compute shaders for both DirectX and OpenGL it's now possible to implement many algorithms without going through the rasterization pipeline and instead use general purpose computing on the GPU to solve the problem.
For some algorithms this seems to become the intuitive canonical solution because they're inherently not rasterization based, and rasterization-based shaders seemed to be a workaround to harness GPU power (simple example: creating a noise texture. No quad needs to be rasterized here).
Given an algorithm that can be implemented both ways, are there general (potential) performance benefits over using compute shaders vs. going the normal route? Are there drawbacks that we should watch out for (for example, is there some kind of unusual overhead to switching from/to compute shaders at runtime)?
Are there perhaps other benefits or drawbacks to consider when choosing between the two?