Like matter verses anti-matter? If so I think this has actually been considered by physicists hence we tested to ensure that anti-matter responds to gravity in the same way as matter.

If anit-matter had shown anti-gravity effects then gravity may have been just some imbalance of forces in the universe, but it doesn't appear to be that way.

Why would it matter?

A torsion to the right, a torsion to the left mate in circular momentum.

Sounds like complementary spins.