While a limited number of schools only accept one exam or the other, a majority now accept both, so students are free to decide which exam they would like to submit as their representative undergraduate admissions exam.
Generally we advise a fairly simple approach to deciding which exam to take: Simply submit whichever test benefits you more. If your percentile score is higher on one exam, then you should choose to submit that exam. Of course, the only way to determine which exam will benefit you more is to take a practice test of each exam type, and see how you score. Of course, if you haven’t yet taken either test and want to know which you should consider, here are some more general guidelines:
The SAT tends to benefit students who are quick-witted, naturally gifted intellectually, test well, and have an exceptional grasp of arcane vocabulary and formal grammar. Conversely, the ACT benefits students who read well, study hard, and have mastered most traditional high-school curricula and even some advanced math (the math on the ACT is slightly more advanced in certain areas but generally less trick-oriented than that of the SAT). Additionally, the ACT contains a Science section, so if you consider yourself scientifically gifted or adept, the ACT could serve to benefit you further in that regard.
The ACT is a more curricular exam, that is, it tends to test more of the actual material that students have studied in school, and the SAT contains more tricks and strategies somewhat unseen in a normal high-school course of study. And while more students have difficulty finishing the pure quantity of the questions on the ACT, the questions that appear on the SAT are considered slightly more difficult qualitatively.