What makes carbonates more likely to produce a salt in a reaction than nitrates?
If you refer to reaction with acids, you need a base. Carbonate ion serves as a base but nitrate ion easentily does not, in water solvent.
It does not have to be a strong base. A weak base is enough to react with a strong acid like
Carbonate ion is a weak base, but it is stronger than the conjugate bases of many acids. So reactions of carbonates with both strong and weak acids are commonplace.