From my understanding, you get discounts for local shops and travel expenses which can be good depending on what you are doing on your trip. I guess it depends on that more than anything.

AirBnB is easier of you don't know any Japanese and want to book quickly. More and more ryokans are supporting booking through English websites. Rakuten travel, for example, supports English. With AirBnB, everything is quite iffy. You might or might not get a good place to stay; you might be disturbing your neighbors without knowing that you are. Snd you might find out that there are night trains passing the place within 10 meters. With ryokans, the facilities are somewhat minimal, but more than enough. The fare is cheaper than hotels. You get other benefits like on-site onsens, discounts, and also local delicacies as breakfasts. If you are a small group that has time for planning, I recommend looking for a ryokan.