Most elegant way to compare two optionals in Swift

Assuming you're using Comparable entities, this will work on anything:

func optionalsAreEqual<T: Comparable>(firstVal: T?, secondVal: T?) -> Bool{

    if let firstVal = firstVal, secondVal = secondVal {
        return firstVal == secondVal
    }
    else{
        return firstVal == nil && secondVal == nil
   }
}

It's not exactly short and sweet, but it's expressive, clear, and reusable.

You can use !==

From The Swift Programming Language

Swift also provides two identity operators (=== and !==), which you use to test wether two objects references both refer to the same object instance.

Some good examples and explanations are also at Difference between == and ===

On @PEEJWEEJ point, doing the following will result in false

var newValue: AnyObject? = "String"
var oldValue: AnyObject? = "String"

if newValue === oldValue {
   print("true")
} else {
   print("false")
}