Well A-rank means you didn't beat them fast enough, I'm not sure if other factors like getting hurt and such also contribute to this when fighting the EX and SP versions.
The only time your ranking doesn't influence your result is when you fight them the first time at that moment you will always receive an amount of Zenny in ascending order i.e. Ox Fire 1000 Z, Cygnus Wing 2000 Z, etc.
Lastly from what I can tell the time influences the card you receive in the following order SP (fast), EX (medium), Zenny (extremely slow). Unfortunately I haven't figured out the exact times that are needed.