What is the difference?
CORE is grain-free, and inclusive of more meat content. (hence more protein) Super5Mix has a few [grain] fillers.
I know that CORE is protein rich.
Why would I feed one over another?
Grain is not a natural part of a dog's diet, so it is avoided by many.
How do I know which to pick?
The choice is obviously up to you, but I would recommend the CORE.