What is your primary concern? Sounds to me like stability is, if that is true look into summarizing routes, using stub routing and ip event dampening and the underlying cause of the instability.
Comparing OSPF and EIGRP, a lot of this has to do with personal preference and comfort level with either EIGRP or OSPF. Both will do the job well. EIGRP is easy to implement and takes less thought. Take that for what you want.
Now for the technical reasons:
-EIGRP is proprietary to cisco, OSPF is an IETF standard
-EIGRP scales well, takes less memory and CPU. Might be a consideration if running on low end routers.
-OSPF can scale slightly better in larger environments due to areas and based on implementers design.
-EIGRP has also better load balancing tweaks compared to OSPF
-both support secure transmition - message-digest key
-OSPF takes more knowledge to implement well (DR, areas, NBMA, LSAs)
-Both can summarize, EIGRP can anywhere on any interface
-Use different timers, which can be tweaked but that can lead to errors and troubleshooting.
Conclusion: both will do the job very well. But as you are already using EIGRP, I wouldn't change without very good reason. Avoid redistribution unless you have to. BGP is complex and if you don't really know it you may want to stay away. You wouldn't be the first or last company to run regional areas with EIGRP and the core on BGP. If you tweak EIGRP and you are still experiencing instability, only then would I look at changing. See prior discussions on this topic: http://forums.cisco.com/eforum/servlet/NetProf?page=netprof&CommCmd=MB%3Fcmd%3Ddisplay_location%26location%3D.ee89484/1
Keep it simply.
Hope it helps.
Steve