According to a book called,
Railroad Spikes A Collector’s Guide by James M. Joyce, the inventor of the Greer spike claims greater holding power as the main advantage. An advertisement claims a “Keen Ground Point” and a “Separate Driving Head,” but it offers no explanation of the advantages of these features. It was used on the Kansas City, Fort Scott & Memphis RR, the Ophir Loop-Lizard Head Pass portion of the RGS, and the Silverton Northern. The spike was easily bent by the outward thrust of the rail base. There is a suggestion that Mr. Jeffery was disappointed by this discovery and thus discontinued the use of the Greer spike. It is not clear to me why this spike design would bend outward easily.
In post #8, I mentioned finding a three-sided “Bayonet” spike, and that the Smithsonian had one example of this type of spike. Theirs came from the 3-foot-gage Grape Creek Branch of the Denver and Rio Grande RR. The one I found came from the Minneapolis & St. Louis RR.