Impossible to answer as formulated, since Final Fantasy isn't actually one series but two (or two and a half). Dragon Quest is a cohesive series under the same creative director (Horii) from the start, whereas Final Fantasy was only truly Hironobu Sakaguchi's project until IX, with his influence lingering a bit for X and XII but totally vanished for XIII and XV.
The best Dragon Quest games are V and VIII. When the series is at its best it's poignant, funny, and has a sort of fairytale depth to it (the true meaning of the narrative isn't immediately apparent). When the series is at its worst it's longwinded, boring, and shallow (VI and VII are good examples of this). In terms of gameplay, Dragon Quest settled on more or less the right formula early on and has stuck to it with minimal changes. Dragon Quest is good for nostalgia and for an overall solid and competent presentation, but Horii seems to have reached the limits of his narrative powers and more recent installments are narratively uninteresting (though not outright offensively bad like recent FFs or Xenoblade 2).
The best Sakaguchi Final Fantasy games are VI, VII, and IX. At their best, the games he oversaw were innovative, mature, and gripping. At their worst they could be melodramatic, adolescent, and mechanically unsound (VIII is the perfect example of this). Unlike Horii, Sakaguchi took risks with FF - some of those risks paid off and some didn't, but he was overall moving the medium forward from a narrative point of view. In the end, though, the suits in the c-suite destroyed his entire project and the series with it, driving out his protégés in the process.
If Yasumi Matsuno had actually taken over Final Fantasy after Sakaguchi's departure the series would be head and shoulders above both Dragon Quest and Sakaguchi FF. Matsuno is by far the best story writer JRPGs have ever seen. Horii knows his limits as a storywriter and doesn't bite off more than he can chew: Dragon Quest games are lighthearted, simple fairytales, but like fairytales they can exhibit flashes of brilliance. Sakaguchi FF frequently bit off more than it could chew by aiming for a more elevated or sophisticated narrative than it could really deliver on. Matsuno is the lone 90s JRPG storywriter who was actually able to cash the checks he wrote: every one of his games is narratively brilliant from start to finish (except XII because they took him off the project halfway through).
The greatest JRPG of all time, Chrono Trigger, is so great because Horii and Sakaguchi were able to check each other's worst tendencies while bringing out their respective strengths.