Based on what's in your profile I assume you're talking about a 29 gallon tank. It sounds like your tank is about full. If you still intend to add either shrimp or cories, I would go with the shrimp since they are going to remain on the bottom more and the cories are likely to go all over, especially since they have to surface for air. Also, the cories are happiest in groups of 6 or more and you could get away with fewer shrimp.
It would be hard to say that "cories" get along with this or that since there are over 300 kinds. A good place for very detailed cory info is www.planetcatfish.com