It's likely that the stolen Bankais are meant to be used in their "Fusion Holy Modes", seeing as they don't have access to the Bankai's advanced forms and techniques (it would be strange for the Sword Spirit to teach and show them how to do it, though they might be able to force them out, probably depends on Quincy's power).
Regardless for what reason, the Quincy steal the:
- Bankai (it's obviously shown),
- Bankai's reiatsu (mentioned by Unohana),
- the Sword Spirit (proved by the fact that Hitsugaya can no longer communicate with his Zanpakutou).
In a way, they obtain special power and reiatsu generators, which for Quincy, who depends on surrounding energy, is a great boost in fighting potential, since they tend to have less spiritual power within themselves compared to Shinigami.
It's also worth mentioning that the Shikai forms are left intact (for example Sasakibe's rapier form), but there is no longer any power in them (the spirit is stolen after all). In other words, they could be compared to remodeled Asauchi (though they likely no longer can become anything else).