I know that the two tests are pretty different, but will studying for the SAT make you more prepared for the English, Reading and Math sections of the ACT? I've already taken the SAT, but I want to try out the ACT too, and I'm not sure what my game plan should be or if I even need to study more.
Prep for the SAT (which you must have taken in its old form) will only be helpful for the ACT in a few small areas. The ACT tests most of the same grammar rules, so if you studied the rules you needed to know for the Writing section of the SAT, you'll be slightly more prepared for ACT English. SAT Math practice could also be helpful, although ACT Math asks questions in a more straightforward manner and contains some slightly more advanced topics (trigonometry, for example). SAT Reading and ACT Reading are very different. SAT Reading tends to ask more complex, confusing questions, while ACT Reading is more fast-paced but less tricky.
The main difficulty that many students have with the ACT is pacing. You get less time per question overall on the ACT, and there's more to read. Your familiarity with the format will have a strong impact on your score. Even if you prepared extensively for the SAT, I'd definitely recommend taking a couple of ACT practice tests before you jump into the real thing. Time management makes a huge difference!
Side note: This answer describes the old version of the SAT as compared to the ACT. The new SAT (starting next month) is more similar to the ACT in format and content, so in the future prep methods and review materials may sync up better between the two tests.