Oil crops are among the main drivers of global land use changes. Palm oil is possibly the most criticized, as a driver of primary tropical forests loss. This has generated two different reactions in its use in various sectors (e.g., food, feed, biodiesel, surfactant applications, etc.): from one side there is a growing claim for deforestation-free palm oil, whereas on the other side the attention raised towards other vegetable oils as possible substitutes, such as soybean, rapeseed and sunflower oil. We assess potential land use changes and consequent greenhouse gas (GHG) emissions for switching from palm oil to other oils and compare this solution to deforestation-free palm oils. We consider three scenarios of 25 %, 50 % and 100 % palm oil replacement in the eight major oil crop producing countries. Total GHG emissions account for anthropogenic emissions generated along the life cycle of the field production process and potential forest carbon stock losses from land use change for oil crops expansion. Replacing palm oil with other oils would have a worthless effect in terms of global emissions reduction since GHG emissions remain approximatively stable across the three scenarios, whereas it would produce a deforestation increase of 28.2 to 51.9 Mha worldwide (or 7 to 21.5 Mha if excluding the unlikely deforestation in USA, Russia, Ukraine and the offset deforestation in China, India). Conversely, if the global palm oil production becomes deforestation-free, its GHG emissions would be reduced by 92 %, switching from the current 371 to 29 Mt CO2eq per year. Although highlighting the historical unsustainability of oil palm plantations, results show that replacing them with other oil crops almost never represents a more sustainable solution, thus potentially questioning sustainability claims of palm oil free products with respect to deforestation-free palm oil.