Yes, wires do make a difference.
You can ignore anyone who gives an explanation that better cables do not work. Basic physics equations don’t properly explain sound dynamics. The basic equations don’t account for anything.
Also, watch out for any comparisons using Monster Cables. Those cables aren't really any good, and people using those to state that there is no improvement need to look at some other brands. I would agree, Monsters aren’t any better than cheap ones, but that has not been the case with other brands. Actually, I've found that Monoprice interconnects do sound better than the Monsters I have owned.
You mentioned that you were going to try Anticables. I’ve had really good experiences with them. I replaced much more expensive cables with Anticalbes when I moved into my current house. Because of the way the house is set up, I needed to use 45 ft speaker calbes and run the cables through underground conduit (not an ideal setup in any way). But frankly, they sound better than the 8ft cables that they replaced. My wife (who has fantastic hearing, but doesn’t care about equipment--the perfect judge) noticed the improvement right away.
Don’t be put off by the thickness of the cable. The important part of the thickness is the copper core. Actually, cables work better when the core is thick and the sheath is thin. Marketing and cost are better when the opposite is true.
When I was buying these, I had a good conversation with the owner. Frankly, his design explanations made a lot of sense.
I would try them. They have a 30 day return policy if I remember correctly. Return them if they don’t work for you.