Dragon Quest III is one of the most popular games in the series. It can only be considered "among the lesser-played" when it comes to more recent fans of the series.
I think FF III is perfectly charming, but DQ III is the clear winner here. Both games are a little clumsy in their class change systems, but FF's is more fluid and DQ's is more slow-moving. Then when you examine the story (DQ III is one of the most epic tales on the NES, period) and quest design (orbs! vs.... surprise oceans?) DQ pulls ahead.
~Maybe Some Spoilers~
And then you have the worst part of FF III compared to maybe the best part of DQ III - the endgame. In FF III, you have to complete multiple consecutive dungeons with six bosses in quick succession, with no good save opportunity anywhere in that midst. The bits with Doga, Unei, and Xande are kinda neat, and the "lend us your power" plot point might be a seminal moment for the Final Fantasy series, but it doesn't rescue the FF III endgame from sucking. It's archaic and dumb and only masochists and oldschool-elists defend it.
Dragon Quest III has a hella-cool final sequence of events: traveling to the world of Dragon Quest I, finding the Sword of Kings, *almost* rescuing your missing father before defeating Zoma, and making the connection that you are Loto the Hero. Every part of it is awesome, and Zoma is one of the more badass Maou / Archfiends in the series.
So, bottom line, after going on for WAY too long, Dragon Quest III is way better than Final Fantasy III. it wasn't until the SFamicom/SNES games where Final Fantasy has a title run superior to Dragon Quest's games of the same period.