I would lean to toward saying Crane. But lets take a look at the cards head to head that have duel effects printed or the duelist keyword.
Kyuden Kakita vs Mountains Anvil Castle
I think this is a wash. Kyuden Kakita profits from any duel win or lose and potentially helps you win future duels wheras MAC gives a more immediate and wide reaching benefit in addition to helping win duels with the stat boost
So this is an interesting comparison. Crane have more duelists (7 to 5) and more printed duels (4 to 3), whereas Dragon really has two of the 3 most potent duels, imho, in the game, with Toshimoko being the most potent for Crane. Crane also has some versatility to their printed duels in terms of effects and duel types (Pol and Mil). I'm going to give the slight edge to Crane here.
Crane does have two dueling focused holdings, but Distinguished Dojo doesn't see play. This comes down to the Mirumoto vs Kakita Dojos. Both have printed military duels and both are enhanced by duelists. Turning off an ability with the possibility of also bowing if the winner is a duelist is very powerful where as moving a fate from a character to the pool or discarding the fate if the winner is duelist can also be powerful. I give the edge here to Crane as Kakita Dojo has more utility than Mirumoto Dojo.
Seal of the Crane
Again, Crane have more cards focused on duels and have fun things not directly related to dueling (Formal Invitation) that can empower their duelists, I think I give this category to Dragon. Mirumoto Daisho and Justicar's approach and Dragon's general attachment support give them the edge here.
Duel to the Death
Game of Sadane
Insult to Injury
Kakita's Final Stance
Rising Stars Kata
I think this is in Crane's Favor pretty solidly due to number of duels and better duel support, though Way of the Dragon deserve mention despite not strictly being duel related...
Arbiter of Authority
Crane win this category too. Niten Pupil isn't currently legal for Dragon as they don't have a Water Role....
So just going by dueling related cards, I think Crane comes out ahead. Where it becomes tough is Dragon can splash Crane and vice versa. Properly tooled up, Raitsugu is a menace as he can straight up kill guys and might be doing it multiple times per turn thanks to Way of the Dragon. If we are solely looking at the cards, Crane has more dueling cards and more flexible options whereas Dragon has a few, powerful dueling cards.