One must make a distinction between a "second source" and "alternative source" for any component. Second source is a contracted manufacturer who gets access to original technology and original masks to be used in the fabrication of the chips, alternative source is a manufacturer who designs his version of the original circuit and claims to offer same performance. The internal ciruit can differ from the original in many respects, very often the circuit is simplified and some features changed or omitted in order to save real estate on the wafer and shorten/simplify test procedures to be able to cut the price.
So, when comparing different makes of a specific opamp or any other IC look at the datasheets for naked die version and compare drawings of the top layer mask. You will then know if you have a true second source or an imitation. The perceived differences in sound may well to be found there.
Having said this i would like to point your attention to an unfortunately obsolete ex Harris Semiconductor opamp 5101/2/4 and (single, dual & quad) which was made using the dielectric isolation process (THAT is using this same process today). This process is unique in that there are no parasitic PN junctions and allows true "discrete on a chip" fully complementary design. It was a really exellent audio amp but we (yes, i worked for Harris) never used any of the "audiophile" arguments in marketing this product. And AFAIK none of the other IC amnufacturers ever did.
The datasheets are still available on Intersil's website (they are what's left of Harris), both uncompensated and internally compensated version is worth a study. The internal circuit diagram of this opamp could be used as a blueprint for a discrete DIY design. I still have a bunch of these for special projects...