In the three proged one you get leakage protection due to the earth terminal. Any stray leakage currents will be pulled to earth to avoid damaging components and from giving hazardous shocks, so its always better to stick with the three pronged ones.
Adapter outputs are DC. So the Real Power in Watts is given by
W = V * I
Your original adapter has a power rating of 20*6 = 120 W
The two pronged one has a power rating of 19*6 = 120-6 = 114 W
The voltage rating is out by 5% and that is not really acceptable because after voltage conditioning the core voltages might be off by more than their tolerance limits
However the current rating is what decides how much the load is pulling.
The current rating is the same 6A so there might be a marginal overheating of the adapter because of the lower voltage, if at all. Nothing serious.
Whenever looking for an alternate adapter the rule of thumb is make sure that the voltage rating is exactly the same, because circuits are generally designed to a specific voltage.
The current rating should be the same or higher.
If at first you don't succeed, relax. You're like the rest of us.