lab techniques - What effect does vortexing have on a fluid sample that simple mechanical shaking does not?

what specific effect the vortexing has that makes it better than manual shaking

In addition to @bobthejoe's answer about viscous fluids, (manual) mechanical shaking is also less consistent and more tiresome than vortexing.

If the vortexer is always at the same speed and each sample is vortexed for the same amount of time, then the shaking step will be less variable among samples. For example, the vigor of mixing an aqueous soil suspension could potentially affect the amount of aggregate decomposition and release of molecules into the suspension (I don't have a reference for this, but it is good practice to treat replicates the same to minimize any non-treatment effect).

Manual shaking is not only less consistent, it is also tiresome - especially with larger volumes (>=10ml) and large sample sizes.