Even the cheap power meters are usually not that bad. Their limitation is more in limited BW and resolution at low currents.
For a lab supply it's usually less about the efficiency but more about keeping the heating low - it is kind of related, as energy is conserved. Still loss distributed over more parts can be less of a problem.
Yes, but the question is (3rd time I write that

) : is it really any better than a center tapped PSU?
To have at least a quite rough idea one would need:
- at least one of those cheap energy meter
- a pre-regulated PSU
- a constant current load
- beeing disposed to unmount (desolder/unconnect the wires) the pre-regulator + post-regulator for the test sake

Since an ordinary linear regulator is just a variable electronic load
from the perspective of the transformer+bridge+capacitor circuit, to get a good approximation of the power wasted at various output voltages and maximum load one needs just
one measure with an electronic load set to the proper value.
The power wasted at a given voltage by a linear regulator would then be just :
total_measured_power - (given_output_voltage * I_load).
Once known that, one could just measure the power wasted by the pre-regulated PSU at various output voltages and maximum load current.
Of course for power measurement I mean measurement taken at the 230VAC supply.