Joe,
These are two VERY different types of film...
APX 100 is still fairly silver rich, with good but definitely conventional grain patterns. You can get excellent sharpness via acutance developers, but nothing like a e-grain or t-grain film. Grain is always going to be higher. Of course, the toe and shoulder are conventional, too, and not as linear, resulting in what many consider to be a much more classic look and feel.
Delta 100 is an e-grain film, with very flat, uniform silver grains. The grain is incredibly fine, and you can use a strong acutance developer to get terrific sharpness yet without the cost in grain. You also get a very smooth curve - toe and shoulder are short, so you get a less traditional look. YOu also have less exposure latitude, since density increase is linear to exposure all the way up (again, because of lack of big shoulder).
They both have excellent dynamic range. Delta has less latitude for error.
I have my own comments about dynamic range from Ray's thread, none of which are confrontational and all of which are qualifying.
allan