Historically the baseband was the primary processor with full control and the CPU was subordinate. This is because the baseband code was developed by the chip manufacturer so they gave themselves full control over the system to make it easier for themselves.

This may no longer be the case right now as the primacy of the CPU has become increasingly obvious, but it should still be the default assumption since having the baseband in control lowers costs to the chip manufacturer which is their lifeblood.