Hello Joseph
The metric will play a role only when comparing the exact same entries in the routing table. 192.168.0.0/23 and 192.168.0.0/24 are two different routing entries and thus each one has its own metric.
If they were the same and had a different metric, only one of them would end up in the routing table, so you would have no problem choosing which one to use. (Unless of course you use unequal cost load balancing for EIGRP, but that’s a different story.)
The first step when going through the routing table is to get the closest match of the destination address with a routing table entry. The destination address of 192.168.0.1/24 matches more precisely (longest prefix match) with 192.168.0.0/24, so this is used.
I hope this has been helpful!
Laz