Why is the verification of Thevenin's theorem more accurate than that of Superposition theorem?
Why is Thevenin's theorem more accurate than the superposition theorem, experimentally?

The last word in this question is the most important one.

To verify the superposition theorem you measure your circuit voltages and currents several times.  Each measurement implies a measurement error.  The error is generally a number of fixed digits and a percentage.

Other errors are also introduced: your measurement equipment is not necessarily linear - the devices introduce possibly non linear impedances.

Every measurement will also include thermal noise.  You will add this up in superposition, but measure it only once for a global measurement.

So once you add up all these errors in superposition, your total error will be bigger than when you make a single measurement.