DQ is a more traditional experience
I would say that the DQ has always taken a back to basics approach to the series proper (I'm not looking at games like Rocket Slime, Torneko, etc, in this argument). The core series has always clung onto tradition computer RPG conventions from battles where you simply choose between melee attachs, spells, and items to use, following quests and story archs in a fairly linear manner, and storylines that pit the player against a particular demonic big bad at the end of the game.
Final Fantasy, on the contrary, has always tried to do something different in each new game. The stories are never interconnected from one major FF to the next. The battle systems have constantly evolved, especially from FFVII to present. Square has tried tossing in several different mini-games, and prides itself on constantly trying to push a console to its limits in terms of graphics.
I just look at the two series as being opposite sides of a coin. DQ has stuck to core RPG dynamics, never trying to veer too much from them. This has given the series a much more nostalgic, old school flavor. Meanwhile, FF is constantly trying to do something new, representing a far more progressive approach to the genre.
As long as someone unfamiliar with either series doesn't go in expecting features or design principles more common in one game than another (ie. playing DQ and expecting a FF experience, or vice versa), they should come away entertained. I've always liked both series simply because they take such different approaches to JRPGs.