They are reborn, unless they are killed by a Quincy
When Shinigami destroy a Hollow they purify the soul and allow them to enter Soul Society. Though I'm not sure if they're reincarnated. The exception is if the Human was evil prior to becoming a Hollow, then they go to hell.
A Quincy's power is utilized using energy to obliterate their enemies. The soul of the defeated aren't purified, so they just dissipate or just plain destroyed. This also disrupts the balance of the world. Hence Soul Society's decision to wipe out the Quincys.