The way you worded that confuses me a lot. I mean, yeah, people tend to do worse on one or the other and not get identical scores, but I would really disagree that going from the SAT to the ACT makes you score lower.
I took the SAT twice and followed up with the ACT WITHOUT writing and then the ACT WITH writing. Every test my score went up except the last one. I would say that the more tests you take, ACT or SAT, your score should go up a little because you get a little better at the little things that make slight differences, such as not being stressed out on the multiple choice.
I also prefered to take the ACT WITHOUT writing first because the writing mindset tended to hurt me once I got to the MC section. This theory of mine proved true, and I only dropped points to include the writing.