The American Heritage® Dictionary of the English Language, Fourth Edition. Copyright © 2003 ( http://www.thefreedictionary.c[..
.] ) says that, basically, both terms denote the act of transporting something from one location to another (transportation, conveyance). However there are a few meanings "transferral" does not have :
a) (figurative) the act of transfering something from one form/state to another ("the transfer of the music from record to tape")
b) (figurative) the application of a skill learned in one situation to a different situation or the link of a psychological response learned to one stimulus to a similar stimulus
c) a person or object ("the best student was a transfer from LSU", a ticket that allows a passenger to change conveyances)
However, I have my doubts as to whether this distinction is strictly adhered to in everyday language. Just to cite one example, the meaning "to seek a transferral of criminal proceedings" is not covered by the AHD "transferral" entry.