Final answer:
Activity-based budgeting is the method used to weigh the costs of an initiative against its strategic importance, helping to prioritize spending in alignment with company objectives.
Step-by-step explanation:
The budgeting method based on an HR leader comparing how much it costs to complete an initiative versus its strategic significance is Activity-based budgeting. This method requires evaluating each activity or project in terms of its strategic value and the resources required to implement it. Organizations use this to prioritize spending and align resources with their strategic objectives effectively, ultimately ensuring that funds are allocated where they can create the most value.