There should not be much of a difference between the lens qualities. The size of the fresnel lens is definitely what would be affecting the light qualities. Is the opaqueness of either fresnels equal? Or is the Strand more diffused than the Arri?
I wouldn't bother lining the inside with foil on the Strand. I don't think it would make a noticeable difference, and on a 2000w light, it could definitely burn the foil or raise the temp inside the house enough to continuously burn out your bulbs. I've seen foil lined 1000w soft boxes burn off the foil... not too much fun.