Total noob question: The difference between OSPF and EIGRP (besides the fact that one is Cisco's baby and the other isn't)

Been looking into it all morning and can't seem to grasp the difference. Even though EIGRP is supposed to be a distance vector protocols, it still works in a similar way to OSPF. Both keep some sort of database and the only real difference (that my slow brain can see) is the convergence time...

If that really is the only difference between the 2, then what causes the difference in convergence time? how does each protocol behave in case a link is lost?