What each one does
Carrageenan reacts specifically with casein, so a very small amount builds structure in a dairy system. Gellan does not react with protein at all; it builds a weak network through the whole liquid that holds particles up while staying invisible in the mouth.
What decides it
Whether the requirement is body or suspension. A dessert that must eat rich wants carrageenan. A drink that must stay clear and thin while keeping cocoa off the bottom wants gellan.
Where the obvious answer is wrong
The obvious answer in a plant based dessert is carrageenan, because that is what the dairy version used. Without casein there is nothing for it to react with, and the level needed rises to the point where the texture becomes rubbery. Gellan is usually the better starting point there.
