EGRP - Exterior Gateway Routing Protocol

EGRP was created to solve many of the problems with RIP and has become the default routing protocol across the Internet. EGRP is an enhanced distance vectoring protocol, it uses up to 5 metrics (conditions) to determine the best route:
Bandwidth
Hop Count (Delay) - maximum of 255
Maximum Packet size
Reliability
Traffic (Load)
These routing metrics are much more realistic indicators of the best routes compared to simple hop counts

OSPF - Open Shortest Path First

OSPF is a link state premise, this means that it has several states of routers linked together in a hierarchical routing model:

The top of the root is the Autonomous Router, it connects to other autonomous systems (the Internet). The next is the Backbone Routers, which is the highest area in the OSPF system. Border routers are attached to multiple areas and run multiple copies of the routing algorithm. Last is internal routers which run a single routing database for one area.
Basically, by dividing the network into a routing hierarchy, substantial reduction of routing update traffic and faster route convergence results on a local basis. Each level has a smaller routing table and less to update.