The big operative difference is that under the Control regime, the regulator decides what practices are acceptable. Under the Liability regime, the acceptability of practices depends more directly on their effectiveness (with more or less directness depending on the type of liability).

A Liability regime would encourage companies to be actually secure, because they're responsible for what happens to data that is lost. A Control regime would encourage companies to check boxes from a list provided by a regulator. A Liability regime encourages being pro-active vs reactive to the regulator in a Control regime.

There are middle grounds, like HIPAA or GDPR. Both give companies some leeway in terms of creating their own checkboxes, and fines are for actual breaches, not just improper process.