Which method is better for our company, the session-based or the fixed-price system?

We are reviewing the budget for implementing an EAP next year at a company with approximately 450 employees. We have a headquarters and two business locations, and shift workers make up about 30% of the total workforce. As this is the first time we are introducing this service, it is difficult to predict the actual usage rate.
Upon reviewing the vendor proposals, I found that both a method of determining the annual number of counseling sessions per employee and a fixed-rate method that settles usage within the total budget were presented. While the session-based system appears to have a clear budget structure, I am concerned about additional costs if there is a surge in users; on the other hand, the fixed-rate system could appear to be a waste of budget when utilization rates are low. Currently, in addition to psychological counseling, we are also comparing managerial consulting and crisis response services.
For a company introducing EAP for the first time, what criteria should be used to compare the session-based and fixed-price models? I am also curious about how to identify and verify expected utilization rates, sessions per person, unused budget, overuse, crisis counseling, and manager support within the quotation.