The IB diploma is harder than AP (depending on what classes you take obviously... Math Studies can't compare to BC Calc, but in general the IB HLs are much longer/harder/more work).
It may be more work, but not really harder. I would say in some ways it's easier because you have tons of time to do some of the stuff that gets counted for your IB grade, whereas in AP it all depends on the exam.
The SAT, after IB exams... is nothing. The New Writing SAT gives you 30 min (?) to write an essay. Try History paper 3. Two hours, three essays.
It's too bad that the Writing Section is only ONE section of the SAT. Doing well on IB won't help you much in the CR or sentence completion sections. Even for the math, it won't help you much because you don't practice the basic-arithmetic-intensive (I use the word "intensive" loosely) that much in IB math (which lets you use your calculator a LOT, along with data booklets).
Even for the Writing section, it won't help you that much. Maybe it'll help you in terms of being able to transcribe your thoughts faster and neater onto the page, but the Writing section of the SAT looks for different things than what the IB history or english exams look for. The SAT essay is graded mainly on mechanics with little emphasis on the ideas. The IB essays are graded largely in the opposite fashion.