This is a very subjective question. Here is my very subjective answer, according to my tastebuds and preferences:
1) The Hardy Chicago Type Figs. Sweetness, flavor, productivity, soft texture, length of harvest season, tree vigor and adaptability... these trees have it all. If I could only have one fig tree it would have to be my favorite Hardy Chicago Type.
2) Barnissotte. Large delicious figs. Extreme richness that lingers on the palate. These figs are a special treat. Just awesome. The downside is that the tree is not that healthy or productive.
3) Black Madeira. Delicious, large, complex flavored figs. Filled with a wonderful syrup. Tree is small but productive. Still the gold standard.