I think, differential swell test would provide more reliable swell index result. Free swell will overstate the extent of the swelling. No doubt the free swell test will give some measure that the soil is prone to swell.
I think differential free swell test give better result because in DFST kerosene is used to note down the original volume of soil which make soil free from atmosphere moisture which may cause swelling of soil. So due to kerosene used we get accurate initial or original volume of soil