What each one does
Starch builds viscosity by swelling granules, which gives a full, opaque, food like body. A hydrocolloid builds it by dissolving long chains, which gives a cleaner, more transparent viscosity at a fraction of the level and far more tolerance to acid, heat and shear.
What decides it
The process and the mouthfeel wanted. Hydrocolloids win on robustness and cost in use; starch wins on texture, cling and the body that reads as a cooked product rather than a thickened liquid.
Where the obvious answer is wrong
The obvious answer is to pick one. In practice most industrial sauces use both, because the starch gives the body and the hydrocolloid protects it through the process the starch alone would not survive.
