EIGRP (Enhanced Interior Gateway Routing Protocol) uses a composite metric that considers both bandwidth and delay to determine the best path for routing traffic. This metric is calculated using a complex formula that includes these two main components, among others. OSPF (Open Shortest Path First), on the other hand, uses a simpler metric that is based solely on bandwidth. The cost of an OSPF route is inversely proportional to the bandwidth of the link, with higher bandwidth links having a lower cost.