Because of the service intervals, the ranges for Heathrow - Central London travel are
Hex 15-30
TfL 30-60
Tube 40-45
So the Hex is always fastest, and the Tube is a slightly better bet than TfL. (I've assumed figures for the Tube are to Earls Court - the first Zone 1 station on the Piccadilly Line. Paddington would take longer).
However, if the first train out is a TfL, waiting for the Hex will only save you ten minutes. If the first train out is a HEx, waiting for the TfL will cost you 25 minutes, or 40 minutes if the second train is another HEx. Forty minutes might be worth paying the extra tenner for.