Actually, HV and LV MVA at any point in time, for a loaded transformer, will hardly be equal – if accurate measurements are taken. Firstly the %Z is a contributing factor, this being mainly inductive generally speaking. Secondly, is the load and its power factor.
Another consideration though, is the action of the tapchanger. By way of example, consider a 33/11kV, 28MVA transformer (sorry I live in the IEC world so ANSI voltage levels do not readily come to mind). Nominal tap = tap7 = 33000 to 11000. Turns ratio is 3.
Maximum tap = tap 17 and corresponding nameplate voltage is 28875kV, i.e. turns ratio is now 2.625.
Now suppose the LV is loaded to rated capacity, i.e 28MVA. ILV = 1470A (assuming the LV voltage is about nominal voltage). IHV = 560A. HV voltage is at system voltage which is 33kV. Thus MVA in HV winding is 1.732 * 560 * 33kV = 32MVA. 4MVA is thus lost in the transfer of power from HV to LV! Admittedly this is a hypothetical question and in reality the actual discrepancy will be determined by %Z, power factor of %Z, tap position, power factor of load, etc. It may not be as much as 4MVA but 1MVA would be quite possible.
Regards.