It's not really to do with the actual metric used ie. hop count, bandwidth etc..
It might help to look at it the other way. OSPF is a link state protocol. What this means is that within an area all OSPF routers receive information about every link in that area (LSAs). So every OSPF router in an area knows about every link in an area. Then each router independently works out the best path from a -> b within an area.
Compare this to a distance vector protocol. Distance vector protocols do not have information about every link within the network. A router running a DV protocol simply relies on it's neighbors to send it routing information and then works out it's best path based on that information. It cannot independently work out the best path because it does not have a full view of the network ie. it is relying on it's neighbors view of the network and it's neighbors rely on their neighbors view of the network etc.. This is known as routing by rumour.
EIGRP does have a topology database but this still is not a complete picture of the network, it is simply a list of all the routes received from all it's neighbors whether they are installed in the routing table or not.
Edit - just in case there is still some confusion about what i mean with links -
within an area OSPF floods router LSAs (type 1 LSAs). Included in this LSA is the cost of the interfaces. So each router sends these LSAs and they are copied to all other routers within the area. This means that every router knows the cost of every link within that area.
EIGRP uses bandwidth and delay ie. minimum bandwidth on the link and total delay so -
R1 -> 100Mb -> R2 -> 1Gbps -> R3 -> 1Mb -> R4 -> 100Mb -> R5
when R1 receives an update from R2 the update will include the minimum bandwidth of 1Mb, It will also include the total delay from R2 to R5. But R1 still doesn't know where that minimum bandwidth is along the path and it doesn't know what each delay is at each router. It simply knows the total delay. Compare this with OSPF above where each router knows exactly what the cost is at each hop.
Jon
