How "over-engineered" were old planes and how "over-engineered" are they now that we have more advanced testing and research options?
You are right that older designs used (and needed!) higher safety margins. I would, however, not call this over engineering. But that is besides the point.

The biggest advances have been made in materials! Not just new alloys, but much better quality control in manufacturing. The aluminium sheets and slabs you would get from a factory 50 or 80 years ago had much greater variations in local strength, and in strength between different production batches. The same goes for fasteners, forgings, whatever. Computer-controlled manufacturing and the relentless effort to improve quality and consistency have made this possible. Only wood is still the same as it was then, but Basil Bourque is right: Processing the wood has also improved by leaps and bounds.

But now consider what we do when we stress a wing: We use the maximum static lift coefficient, add aileron deflection and use that bending moment at v$_A$ to size our wing spar. We do this by applying a safety factor of 1.5 (§25.303). For parts with a more error-prone production process additional factors need to be added (see §25.619).

And now consider what happens in the real world: The dynamic maximum lift coefficient, which does not obey the rules and regulations imposed by the FAA, will easily be 1.3 times bigger than the static lift coefficient used for stressing the wing spar. In tests up to 150% have been achieved. Makes you think how sensible that safety factor really is. While we understand the static loads very well (because they are easy to study), dynamic and fatigue loads still happen to surprise the engineers from time to time. A little extra margin sometimes can be quite useful.

On the Eurofighter the structural safety factor was indeed reduced to 1.4 with the reasoning that more precise modeling and simulation would allow to use a smaller margin.