Do you care about duplicate counts? For example, would you need to distinguish between { 1, 1, 2 } and { 1, 2, 2 }? If not, just use a HashSet:

public static boolean compareArrays(Integer[] arr1, Integer[] arr2) {
    HashSet<Integer> set1 = new HashSet<Integer>(Arrays.asList(arr1));
    HashSet<Integer> set2 = new HashSet<Integer>(Arrays.asList(arr2));
    return set1.equals(set2);
}

If you do care about duplicates, then either you could use a Multiset from Guava.

If you want to stick with the sorting version, why not use the built-in sorting algorithms instead of writing your own?

EDIT: You don't even need to create a copy, if you're happy modifying the existing arrays. For example:

public static boolean compareArrays(Integer[] arr1, Integer[] arr2) {
    Arrays.sort(arr1);
    Arrays.sort(arr2);
    return Arrays.equals(arr1, arr2);
}

You can also have an optimization for the case where the arrays aren't the same length:

public static boolean compareArrays(Integer[] arr1, Integer[] arr2) {
    // TODO: Null validation...
    if (arr1.length != arr2.length) {
        return false;
    }
    Arrays.sort(arr1);
    Arrays.sort(arr2);
    return Arrays.equals(arr1, arr2);
}

You can do in a single loop with Arrays.equals() method.

public static boolean checkIdentical(int[][] targetArray) {
    int[] prev = null;
    for (int[] a : targetArray) {

        if (prev != null && !Arrays.equals(a, prev))
            return false;

        prev = a;
    }
    return true;
}

need to import java.util.Arrays.