I've already taken the SAT three times, but I also plan on taking the ACT to make sure I'm not missing out on a higher score. Is the ACT essay a lot different from the SAT essay, or are they pretty comparable? If there are major differences, how should I adjust my approach/practice methods to make sure I do well?
Yes, the two essays differ in a few significant ways. The ACT essay (or Writing section, as it is formally called) is 40 minutes long. The prompt will describe an issue and then state three different perspectives on it. Your job is to evaluate and analyze the given perspectives, state and develop your own perspective, and explain the relationship between your perspective and the perspectives provided by the prompt. You can argue one of the positions given by the prompt or come up with your own stance on the issue.
The (old) SAT essay presented a slightly different challenge. On the version of the SAT that you most likely took, the essay prompt posed a question and asked you to write a response detailing your opinion on the topic. This might seem similar to the ACT essay, but on the SAT essay you didn't have to analyze other perspectives in addition to your own. On the ACT, you'll have to provide more than just your opinion supported by examples - you also have to explain up to three other possible perspectives and relate them to your views on the issue. That's why the SAT essay was only 25 minutes as compared to the ACT's 40 minute time allotment.
The best way to prepare for the ACT essay is to practice responding to real prompts. Be aware of the fact that you need to explain the other viewpoints, not just your own, and contextualize your position. You can consult the ACT site for practice prompts and examples of successful essays.
Additional note: The ACT essay differs even more drastically from the current SAT essay, which asks you to read a passage and write an essay detailing how the author builds his or her argument. The new SAT essay tests your reading comprehension and ability to analyze a challenging writing sample in a logical, well-organized way. The ACT essay still asks for your opinion on a topic.
Sources:
http://www.act.org/content/act/en/products-and-services/the-act-educator/about-the-act/act-plus-writing.html
https://collegereadiness.collegeboard.org/sat/inside-the-test/essay