Safety policy of a firm - clarifies rights , assigns responsibility as well as accountability across all verticals in a management. Which approach is better in implementing this policy ?

For implementation of any policy or change ,Organizational & Stake holder integration and participative approach is always better.

Start from the top management and embrace it down the line. Make sure it is well understood and accepted. The Policy is the basis for your health and safety management system.

The best approach is a planned and systematic approach that implements health and safety efficiently  efficiently through a health and safety management system