It was obvious to me too, right away listening to the first singer, on the first word of comparison. However, it sounded maybe a bit louder too, which would favor the neve and make it sounder better no matter what. Definitely the richness and harmonic character is there.
Seems like you are chasing your own tail. I like the microphone recording standard sweeps idea from Ian, in a controlled setting.
I've also worked with original Neve modules that sounded like a damp blanket, and others that had the magic. This means to me it's got to be a setting. It's not the actual Neve manufacture or traces or iron, or the layout, wires, or any part, etc. (Well iron maybe -- I should correct myself -- there are differences from different companies which may make some diff like St Ives vs Marinair... vs Carnhill... but it's not going to be big difference like you are experiencing.)
Beyond that, I believe it's a setting, not a construction element or part that is causing the differences. If two original Neves can sound so different, one right and one wrong, then it means it's not the parts or the construction. There are obvious variations like zobel settings and hookup settings, input Z setting, output amp bias setting, and power supply variables. Power supplies DO effect sound. (Have you made controlled tests with same PS and diff modules, and same module and diff PS?! You may be surprised.)
I think you need to find the common variable that is consistent with the tests, as Ian said. Any of the variables I mentioned above in preceding paragraph can cause the blanket and other effects you have complained about.
It may be one of those, rather than a more esoteric and elusive one. I know from my own troubleshooting that I often overlook the actual fault even when I collect the data that could identify it, because I am looking elsewhere or convinced that I have to find a certain type of fault, etc. It often takes an outsider with no agenda to steer me back to the obvious fault.