Can Rock Band DLC transfer across console brands?

No. DLC does not transfer between different console brands.

DLC is tied to a specific console platform and cannot be carried over to another platform.

For example, moving from Wii to PlayStation, or from Xbox to Wii, will not transfer DLC.

Note: This does not apply when upgrading or replacing the same console type. In most cases, DLC can be transferred to a newer or replacement console within the same platform family.