RIP is a distance vector routing protocol that chooses the best path as the one with the lowest number of hops, regardless of bandwidth. It converges slowly and has limitations on path length. OSPF is a link state protocol that calculates the best path based on bandwidth and uses the Dijkstra algorithm. It converges faster but places more load on routers. Both protocols periodically share routing information but OSPF only sends updates for changed routes while RIP sends the whole table.