I'll pipe in, my opinion is free, and maybe worth exactly what you paid for it...
Side mount is a very finicky thing. I can dive the same set up, everything the same, and it be great one weekend and wonky the next. If I have a bad case of gas, it changes my trim.
I am assuming you are swapping regs and breathing both tanks down evenly...
So it sounds like you are diving 2 different tanks maybe from 2 different manufacturers...? Diving matched tanks would probably help. If the tanks have markedly different buoyancy characteristics, you may need to compensate for that. Even if you were diving matched tanks but still listing to the right, moving weight around is usually an option, depending on your rig. If you have weight on both hips, move some from the right to the left so that the more lead on the left off sets the less buoyant tank (that you have on your right).