First game, Final Fantasy. The first DQ is rough, and not in a fun way. FF1 isn't the best of the Famicom games, but it's good.
Second game, Final Fantasy. I actually really like FF2, even if I do agree that it's SaGa Zero. And don't listen to people who talk about stat grinding by beating yourself up; the game is beatable without any stat grinding.
Third game, Dragon Quest. Much as I like FF3, it's not even a contest.
Fourth game, unsure. There's merits towards both being better than the other. If I had to choose one, maybe Final Fantasy? But I could also turn around and say Dragon Quest ten minutes from now.
Fifth game, Dragon Quest. Not even a contest. For everything neat FF5 did, DQ5 is better. The story is great, monster recruitment for your party is good, if a little iffy, Deborah in DS is great, etc etc.
Sixth game, Final Fantasy. Not even a contest. DQ6 is kinda mediocre, even if it does have some neat things (if you keep rejecting getting your corporeal forms back, the witch eventually tells you that you'll do it anyway, because you have no choice. But you do it without Milayou, because you said you weren't going to), but it's a passable game compared to the start of FF's golden age.
Seventh game, Final Fantasy. I adore DQ7, and consider it the second best in the series, behind 5. FF7 is just better, however. Coming from someone who hated it until they played it in 2019 after being disappointed with Remake.
Eighth game, Dragon Quest. I'll be honest, I don't care for DQ8 that much. It was my first DQ game, and it made me think I disliked DQ until I was told DQ5 was like an FF game. Which made me try DQ9, which made me realize my issue is DQ8 and not DQ. I just really dislike FF8's combat, to the point it's soured me on the rest.
Ninth game, Final Fantasy. FF9 is one of my favourite games, and so DQ9 isn't going to compete. It's a very good game; it just has extremely stiff competition.
Tenth game, Final Fantasy. Last great FF game; not that it matters when its competition is a region locked MMO. Interestingly, I hated FF10 for two decades because I couldn't ever manage to stay interested enough to play after the Chocobo Eater. I finally just forced myself to keep going, and ended up loving it almost as much as FF9.
Eleventh game, Dragon Quest. I never played DQ11. I just know my friends love it, and its competition is an MMO.