Why should there be a significant difference between a WHM/CON and a WHM/THM? They are both White Mages. Was there a significant difference between a WHM/BLM or a WHM/RDM? In each case White Mage defines you as a party-support/healing class.
There is however a big different between a WHM/CON and a DRK/LNC. That's the difference that matters because you would expect that a WHM would be very different from a DRK.