[Dekatron]

Measure both AC & DC voltages so that you can see how close they are between the testers (or how far off).

The correct Grid voltage in the Mk III can only be measured with the valve removed and the "SET mA/V calibration" link open so you only measure the negative period used for grid voltage and not the extra negative period that is added for the use of leakage/shorts tests.

Also make sure that the meter you use can measure half wave rectified voltages properly on the DC and AC ranges.

If you have an oscilloscope (connected to an isolating transformer so you accidentally don't form shorting ground loops) you can check what the voltages looks like with the valve under test - there is a slight chance that testing an EL84 results in it oscillating (more so if you measure the voltages present with long wires to the instrument), which will result in strange readings. This is why using a triode as a "calibration" standardized valve is a better option as they are harder to get to oscillate while being tested.

When you get correct DC-readings for both testers you can use those with DC power supplies to see how the EL84 performs under those conditions to try to rule out if any of the testers shows incorrect readings at those voltages, or if there might be something else that is incorrect. Don't forget that the EL84 might oscillate with just DC-voltages present, so short wires and possibly grid stopper resistors and capacitors close to the socket and other means to hinder oscillations might be necessary there too.