The big company might well have better quality control (though, depending on the regulatory environment, you may have very good grounds to believe that everyone's quality control is good enough) -- but it seems unlikely that the same big company has better quality control for one product than for another identical product in different packaging.

But not impossible. You could imagine that they do some kind of tests on their pills, and put the "better" batches in the fancier packaging with the higher prices. I doubt it, though. (Though I bet such things do happen in other less tightly regulated markets.)

One area where it happens is electrical components; for instance, if you buy a bunch of 10kΩ ±5% reistors and measure their actual resistance, you should find a nice distribution with a big hole around exactly 10kΩ; those resistors were taken from the batch and sold as ±1% (or better) tolerance. But it shouldn't happen with drugs, I doubt there are "grades" of acceptable quality.

You're right about the placebo effect, I'm sure I once read about a study that found patients reported better pain relief from the pills with fancy packaging. As you said, we're dealing with pain relief which is inherently subjective, so the placebo effect matters.

My girlfriend is a doctor, and often goes for the branded versions, saying they will be better quality, and absorbed better.

I have read before that good quality vitamin pills are bigger so that they crumble / break down and get absorbed better that hard compact ones.