I am putting a GDT in parallel with TVS diode, and I want to know if I need to have clamping voltage of TVS diode slightly higher than DC breakover voltage of the gas discharge tube OR have clamping voltage and DC breakover voltage the same.
A GDT is slow compared to a TVS hence the TVS should be chosen to activate first when the surge is rapid. That’s the aim and to achieve that, you must have a sufficiently high clamping voltage across the TVS so that the GDT will (eventually) trigger a few micro seconds later. This means that the TVS clamping voltage must be greater than the GDTs slow spark over voltage. By how much is down to the designer.
If the surge is slow, then the GDT will activate before the TVS and, under these circumstances, the TVS will never be called into action because the GDT will have sparked over and fold-back limited the surge to a few tens of volts. The TVS is there to handle the fast edge and then the GDT takes over to handle the bulk of the surge energy.