Inside Cabinet Speaker Cable Causing A Big Difference in Sound

I love it when there are "big differences" no measurements and lots of discussion. So great. So a big difference would be like 6 dB? I'm thinking cold solder joint, maybe a loose connection. We're talking "A Big Difference in Sound". Different wire would be the very last thing on my list to look at, unless that wire has two ohms of resistance or something that is a big difference from the other wire.
 
Screw terminals?
I would suggest mounting them firmly, away from the speaker, to avoid damage to the actual speaker terminals, as most will not stand up to repeated mechanical stress caused by screwing and unscrewing wires.

Or use set of terminals as above.

But if you want to scratch your itch for testing wires, use an offset pair of terminals, mounted separately to the cabinet, and one set of wires permanently soldered to the speakers.
Then you can experiment without fear of damage to the speakers. Just change the wires at the terminals, and you can use spring loaded terminals as well, very convenient.

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Image off the net, no ties to seller.
Use an appropriate one as per your cable size.