Security of randomized data dependant key schedules?
Data-independent key schedules allow the round subkeys to be computed once in advance.  They can be reused for each subsequent block you encrypt.  This potentially allows significant performance speedups.

Data-dependent key schedules don't have that property.

Otherwise, there is no fundamental difference.

Normally, the key schedule is defined or understood to be the part of the cipher that depends only on the key and can be computed in advance (doesn't depend on the data).  So, "data-dependent key schedule" is somehow a contradiction in terms.