They're nature and breeding group.
Edit: so it turns out its the ID number and species. I did read somewhere that nature affects it
Same species with different ID numbers:
Chance of getting an egg; 70% | Statement; "The two seem to get along very well!"
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Same species with same ID numbers:
Chance of getting an egg; 50% | Statement; "The two seem to get along"
__
Different species with different ID numbers:
Chance of getting an egg; 50% | Statement; "The two seem to get along"
__
Different species with same ID numbers:
Chance of getting an egg; 20% | Statement; "The two don't seem to like each other"
__
Different Egg Groups:
Chance of getting an egg; 0% | Statement; "The two prefer to play with other Pokémon more than with each other."