In OSPF, when a router learns about an external network through both E1 and E2 advertisements, and if both have the same path cost, the router will prefer the E1 path. This is because E1 routes consider both the external cost to reach the external network and the internal cost to reach the ASBR, providing a more comprehensive metric. E2 routes only consider the external cost and ignore the internal cost to the ASBR, which could potentially lead to suboptimal routing. Therefore, the router will choose the E1 path due to its more accurate representation of the total path cost.