What is 'equality' of chemical bonds?
For $\ce{CO_3^2-}$ you have the following possible resonance structures:



The structure bellow, is the one which represents better the real ionic molecule, in which all the bonds are equal. You can delocalize the negative charge through all the ion.

For $\ce{H2CO3}$ the structure is:



As you can see, in this case, bonds are fixed, and there is no possible resonance delocalization, so you have two single bonds (less strong) C-O and one double bond C=O (stronger). For $\ce{CO_3^2-}$ you have that all bond lenths the same showing an intermediate situation between single and double bonds.