Final Fantasy vs. Dragon Quest II
I have to give this one to FF. I can enjoy playing FFI again and again but DQ II always feels more like a chore to play through. It has its few moments but for me personally it doesn't stack up against FF I.
Final Fantasy II vs. Dragon Quest III
Dragon Quest III all the way. Nothing in FFII even compares to DQ III. It's my personal favorite of the NES generation.
Final Fantasy III vs. Dragon Quest IV
DQ IV takes this one. Far better story-telling, more enjoyable characters, and over-all it's just a much more fun game to play.
Final Fantasy V vs. Dragon Quest V
DQ V wins here too. I find that FF V tends to be mostly forgettable. While the class selection ability was neat it's not something I enjoyed much in FF III or FF V.
Final Fantasy VI vs. Dragon Quest VI (one year off, FF predates)
I'm not sure how to vote this one. I don't have a lot of memories of DQ VI but I also never played it all the way though. Every time I've tried the ROM got corrupted :/
Final Fantasy IX vs. Dragon Quest VII
Final Fantasy IX was an amazing game. The only thing I would change about it would be trance being selectable instead of forced upon you. DQ VII always seemed like the awkward step-child of the series to me.
Final Fantasy XII vs. Dragon Quest VIII (two years off, DQ predates)
DQ VIII wins this by a landslide. It was an amazing game, and something exciting during a time when it was harder to find good RPGs.
Final Fantasy XIII vs. Dragon Quest IX
I've never played DQ IX and have no intention of ever owning the system it came out on.