IPv6: cost metric administrative distance
metric and cost is similar.
the router use the metric/cost to decide which route is the best for a destination.
in ospf terminology we use cost which is calculated from interface bandwidth.
but we use composit metric for eigrp which is calculated from bw and delay by default.
in your ospf domain the routes from eigrp will use the 25 cost on that router in which you perform redistribution. than, depends on E1 or E2, the cost will increase hop-by-hop (E1) or not (E2).
admin distance is the first step to decide the best route.
lower addmin distance is better -> first router choose the route for particular nlri which has a lower AD
lower cost/metric is better -> if AD is equal (learned from the same routing process) lower cost/metric is better