Here's the progression of farms as they appear in the game. All the numbers are from PlanetImprovements.xml.
Basic Farming: Food 4, Cost 50
Xeno Farming: Food 6, Cost 100, Requires Xeno Farm Construction
Intensive Farming: Food 8, Cost 10, Requires Xeno Farm Construction II
Advanced Farming: Food 8, Cost 150, Requires Xeno Farm Construction III
There are also two more farming improvements listed in PlanetImprovments.xml, but they are not in the game because they require technologies that are not currently defined.
Extended Farming: Food 10, Cost 210, Requires Xeno Farm Construction IV
Ultra Farming: Food 12, Cost 310, Requires Xeno Farm Construction V
Several bugs here:
(1) Intensive farming is presumably supposed to cost 120 or thereabouts
(2) Advanced farming is presumably supposed to have more food than the building it upgrades
(3) The devs might intend to enable the final two buildings by adding the corresponding tech.
As it stands, it's absolutely counterproductive to research X.F.C. III, as the player receives no bonus but has to pay a big upgrade cost.