Space complexity comparison shows: 1) Recursive uses O(log n) stack space, 2) Iterative uses O(1) constant space, 3) Each recursive call adds to call stack, 4) Iterative only uses few variables, 5) Stack depth proportional to log n divisions, 6) Iterative preferred for memory constraints, 7) Trade-off between code clarity and space, 8) Important consideration for large datasets.