Speaker Fill replicates the Left/Right audio onto the Left/Right Side/Rear speakers when playing stereo audio files. Nothing more.
Dolby Headphone takes a 5.1/7.1 audio signal and virtualizes it onto a stereo sound space, so you have a stereo signal that is played back in such a way that it appears to be a genuine surround sound audio track.
In theory, both should work more or less the same. The difference is likely in HOW the two methods attempt to virtualize surround audio. Really impossible to tell which is better without an exhaustive test of the two methods.