to me the API sound is Daniel Lanois.... U2's Achtung Baby..
one of my favorite sounding recordings for API/tape/pultec goo is "the man in the long black coat" which Dylan did with Lanois on an obscure record called Oh Mercy in the 80s.
we used to use that to warm up the Wilson/Levinson setups... it sounds GORGEOUS.
a good example of the Neve sound is Meat Beat Manifesto's "Actual Sounds and Voices", at least for synth/sampler music. Viva Jack Dangers!