Simply put, both protect against certain types of interference in different ways, and each is effective in ways that the other is not.

Mesh shielding is going to help prevent electrical interference from being introduced via the wire itself from an external source. Like other cables carrying signal and running very near/parallel, or electromagnetic fields generated from other devices, certain electrical components, household appliances, etc.

The ferrite beads protect against radio-frequency interference (RFI) via induction, acting like low-pass filters which attenuate specific bandwidths of very high frequency signals. Essentially, they intercept and absorb high-frequency electrical noise, and convert that energy into a small amount of heat instead of letting it pass through further down the signal path. This kind of interference can be from an external source, or generated internally from the various electronics/components in the signal path (which mesh shielding would do nothing to protect against). They also help dissipate any RFI that the mesh shielding itself may be carrying, so you often see both ferrite beads and mesh/foil shielding, like on laptop chargers or USB cables for example.