Resource management relates to the management of resources such as time and people. For example, how much time should be spend on each tasks and who are the employees that should be assigned to each task. 

Procurement management is where you identify the needs of the project that can be met by acquiring resources. You would need to consider whether to procure, how to procure them, how much, and when to purchase the resources. This tends to relate more to resources that can be acquired through the spending of money. 

I feel that resource management is more important because it doesn't matter how much you spend on getting the materials if you are not able to utilize them properly or in a timely manner. Thus, it is more important to ensure that the staff are able to work to their full potential and their time is being used efficiently. 

Also, procurement management is a subset of resource management. Resource management refers to all resources whether they are people, skills that employees possess or materials. On the other hand, procurement refers to materials. 

This is why I also agree that resource management is a more general term hence more important.