I agree, Windbane, Final Fantasy is definitely a big property in Japan, but it doesn't sound like you disagree that DQ is bigger there. The actual appropriate way to see which sells better would be a system-by-system basis, as there have been 5 Final Fantasies in the last 12 years, compared to 2 Dragon Quests (although a third is about to join that troop).
The PS2 Dragon Quest outsold the two PS2 Final Fantasies by .6 million and 1.2 million, respectively.
The PS1 Dragon Quest outsold the three PS1 Final Fantasies by .2, .5 and 1.2 million, respectively.
The two SNES Dragon Quests outsold the two SNES Final Fantasies by about .2 and .3 million, and .65 and .75 million respectively (meaning the less popular DQ outsold the most popular Final Fantasy)
The three NES Dragon Quests outsold the four NES Final Fantasies handily (can't tell how much, since the FFs didn't crack a million).
The difference between the two has remained relatively stable over the past 15 years.
Even with this noted, people should absolutely remember, as Windbane said, that Final Fantasy is a bigger deal overall because it sells worldwide, unlike DQ, which is a huge deal in Japan but almost forgotten everywhere else.