If you search online, you can find isolated regulatory incidents, patient anecdotes, and even statements by doctors that they prefer patients not switching brands when something works for them. Beyond that, I'm not sure what is really known, or how you would go about studying this phenomenon in a scientific fashion.

Even if it is a placebo, if two medications that are supposedly the same cause different effects on me, e.g. one has much more manageable side effects than the other, then why shouldn't I take the one that makes my life better?