The tests are not equivalent
Same content, different clocks. The ACT gives about forty-nine seconds a question in maths; the SAT gives roughly twice that. The ACT has a science section that is really a reading-a-graph section under time. The SAT's passages are longer and its maths leans harder on algebra.
Sit one section of each, timed
Not a full test — one maths section from each, under a real clock, on the same morning while the student is equally fresh. Score both and convert to percentiles. If the gap is more than about three points, that is your test and there is nothing further to think about.
What a tie means
Under three points, take the ACT if the student reads quickly and the SAT if they do not. Speed is the ACT's entire personality, and a slow careful reader gives away more there than anywhere else.
Then stop shopping
The most expensive mistake in test prep is preparing for both for two months. Everything after the measurement should be one test, one book and one set of question types.