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Adding a larger diameter wire does not decrease the wires resistance at the lengths we are talking about here. It only adds current carrying capacity which is not needed. Actually a larger diameter wire might ADD resistance to the circuit, depending on its properties.
What the real question is: 'what type of wire is the OEM using?'. Wire is not just wire.
(Now for some speculation) - I would be willing to bet the wire used on both US and Euro O2 sensors is of a specific type of very low resistance wire. Some type of NiCu (nickel/copper for corrosion resistance) wire (not likely) or AgCu (Silver/copper). Silver is a better conductor than copper and way better than nickel.
Then you solder your connection with a generic solder (when you should have used a low resistance solder), which has a much higher resistance value than the core wire, so you introduce a high resistance (higher than the core wire) junction.
It also might not be a resistance issue but a cross-talk issue.
(More speculation)
They use a specific low resistance wire not because they are worried about loss (the effective voltage is .2V to .9V) , but the frequency of the signal. The higher the RPM, the higher the frequency or cross-counts (lean/rich). The higher the frequency of the signal, the more the electron flow gravitates to the outside of the conductor and maybe the sensor signal is bleeding over to the other (return side) of the wire, damping the effective signal to the ECU. All because when you spliced in some other wire, you did not effectively insulate the solder junctions and the 'new wire' is not good enough.
Or it could be both...
Also, with the normal household volt-ohm meters (especially the chepo $50 meters) you cannot reliably measure the wires resistance at these lengths. The values are so small they fall into the mean error of the meter.
Even my $600 Fluke meter will not do it and it is professionally calibrated every six months.
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