You can check to see if the contentSize is larger than the scrollView's bounds.
CGSize contentSize = scrollView.contentSize;
CGSize boundsSize = scrollView.bounds.size;
if (contentSize.width > boundsSize.width && contentSize.height > boundsSize.height) {
// scrollable both vertically and horizontally
}
else if (contentSize.width > boundsSize.width) {
// scrollable horizontally
}
else if (contentSize.height > boundsSize.height) {
// scrollable vertically
}
else {
// same size or smaller, not scrollable
}