If you just want to know if they are different from each other, meaning by length, order or individual items, you can do the following, which first checks to see if the lengths are different, then checks to see if the individual elements are different. This isn't terribly reusable, it's left as an exercise for the reader to split this apart into cleaner chunks :)
public function foo(coll1:ArrayCollection, coll2:ArrayCollection):void {
if (coll1.length == coll2.length) {
for (var i:int = 0; i < coll1.length; i++) {
if (coll1[i].first != coll2[i].first || coll1[i].last != coll2[i].last) {
Alert.show("Different");
return;
}
}
}
Alert.show("Same");
}