The older Fordomatics, (pre 1958) called for Type A automatic transmission fluid. (There is also an aluminum case Fordomatic 2spd that came out in 1959. I don't remember what trans fluid was recommended) Type A has been replaced by several different Dexrons and what is now Dexron III.
Type F fluid came out for use in the new cruise-o-matic transmissions in about 1958. Type F was also used in the FMX and most pre '77 Ford transmissions and in some other Ford transmissions til 1981.
Most oil manufactures list pre 77 Ford's to use Type F as they seem to believe there are no Fords still running that are older than 1958.
Type F has a higher viscosity than Dexron III and a higher heat tolerance. Dexron has more lubricity than Type F which makes a softer shift compared to the Type F which is more firm or harsh.
The key thing is; use what you transmission rebuilder advises as he may has installed the newer bands and clutches that use a material that requires a Dexron III fluid. Also he is the guy who has to provide warranty.
Do not use the newer fluids such as Mercon V which has a very different formula used for the lock up converters.
There is newer Type FA on the market which is supposed to be a replacement for Type F and superior to the original Type F. I am not up to speed on it.
here is some interesting reading on the Type f vs Type A and Dexron fluids
http://www.pennzoil.ca/documents/Automatic%20Transmission%20Fluid.pdf
http://www.hwpetro.com/_fileCabinet/TexacoData/Hav-ATF-F.pdf
http://www.mobil.com/USA-English/Lubes/PDS/GLXXENPVLMOMobil_ATF_Type_F.aspx
http://www.redlineoil.com/product.aspx?pid=52&pcid=9
http://ezinearticles.com/?Use-the-Correct-Type-of-Transmission-Fluid-to-Prevent-Mechanical-Problems&id=4847509
marv