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OSPF is an Open Standard meaning it can been used in a hybrid environment of router. EIGRP is for Cisco Specific. If your environment has all Cisco Routers, it will be good to go with EIGRP but you have multi-vendor product OSPF is preferable.
EIGRP has been released by Cisco recently and now it's a part of RFC publications, so it may exist in all new routers from all brands, but for old routers it will be only in Cisco. EIGRP has a very fast convergence-time, summarization can be done at any point and there is no need for hierarchical design, while in OSPF you can summarize only in area borders and the design will be restricted by Areas.
Therefore, if you have only Cisco routers, the best option (in my opinion) is EIGRP, otherwise OSPF is a good option too
EIGRP is better than OSPF because EIGRP have fast convergence. EIGRP create topology table. In this topology table it have two route one is called successor and another one is called feasible successor. Best route is called successor and another best route is called feasible successor. EIGRP also stored feasible successor route in topology table. When successor route will goes down EIGRP will run DUAL algorithm to scan topology table and take the feasible successor route and add in to routing table. EIGRP provide auto summarization by default
Where as OSPF is standard protocol. OSPF will provide hierarchy topology. OSPF will not provide auto summarization by default.
So; the classic answer is the use of an "open standard" routing protocol in the shape of OSPF, versus Cisco proprietary running on Cisco hardware in the shape of EIGRP.
The core question to ask yourself, though, is whether you need a routing protocol in the first place, and whether or not that justifies the hardware investment and CPU load.
Amongst other things, OSPF is an hierarchical routing protocol, with the concept of areas, and that's where it really shines. But would you believe it if I told you that I've seen numerous clients running OSPF simply to run it in the backbone Area-0 for some basic IGP routing, when something like RIP-2 or even a bunch of static routs would do just as well?The short answer: horses for courses.
It depends on your requirement and your network design and architecture, but in general, if you're working with a pure Cisco solution then consider using EIGRP as it is a Cisco proprietary protocol.
