I've posted another comparison using the new Canon EF Extender III 1.4X, showing how it performs with Canon EF 70-200mm f/2.8L IS II and the Canon EF 70-200mm f/4L IS. See my review in DAP. Next up is the EF Extender 2X.
The EF Extender III 1.4X acquits itself fairly well on the f/2.8 zoom, turning the f/2.8 zoom into a 98-280mm f/4. But whether it meets your needs will depend on the nature of what you shoot.