Does the audio signal pass through a coupling cap?
Why do I hear changes in sound quality between different caps?
1. It passes though in the same way as a wire, though I expect some disagreement on this.
2. Perhaps because you want to.
This is really easy to find out if there are differences and what they are. Take a double pole double throw (6 lug switch) or relay and connect it so you can switch one speaker from one channel to the other. Drive both channels simultaneously. Mono the signal using 20K resistors so the right and left channels don't fight each other. This is common practice in mono-ing a signal. If you don't use resistors you may get a lot of distortion from your preamp. If your preamp has a mono switch use that.
Be sure your amps don't mind being unloaded, most are just fine as long as the input stays constant which it will.
Prove to yourself that your two identical channels sound identical. If they don't you have to work on them till they do. Invite a friend whose ears you respect to join you. He gets the easy part, listening.
Now change whatever caps you want in one of the channels. Listen again. What do you hear?
This is the easiest experiment I can imagine. Get a heavy switch at any electronics or hardware store. A good one is 10 amps with a 1 inch x 3/4 inch body. You can get ones with screw or solder terminals, you can put it in a box with connectors or wires of your choice.
I really encourage you to do this. This is a much better experiment than what is commonly done using acoustical memory with time between changes. Go back and forth a lot at first when you hear something new, check it. Eventually you might leave the switch in one position for a long time. The benefit of the switch is that you can go back and forth anytime without having to get out the soldering iron.
Compare the time it takes to make this little device compared to the time it takes to change caps.