It's a matter of your goals
I think the biggest difference is going to be which agency caters to the type of freediver attending.
I can tell you from first hand that IAFD and S.A.F.E.R. cater primarily to recreational freedve instruction. I am certified by both entities.
IAFD is probably the most mature at this point. They have an excellent program that follows the same techniques of teaching as used in the tank diving programs. S.A.F.E.R. is run by our very own Ricardo Hernandez, who use to be General Manager of the IAFD. His program is also very good and makes a big point of covering safety within the sport.
I have attended PFD and although there were many spearfishing freedivers there, I felt it catered more to performance type techniques. The PFD team does an excellent job in their teaching, although they don't have official certification at this point in time (Kirk, if I missed that point, please chime in and correct me)
I think it just is a matter of what your goals are.
I have not taken the IANTD course yet, so I can't comment on the quality of the program, but with Dan Hodgins and Tara Cunningham teaching this program in the Cayman Islands, I think you would be in excellent hands. I have heard nothing but praise for their teaching style
If you have any other questions, you know where to find me...