You could use the Calculate event and a Static variable

Private Sub Worksheet_Calculate()
    Static vPrior As Variant
    With Range("A1")
        If .Value <> vPrior Then
            MsgBox "New: " & .Value & vbLf & vbLf & "Old: " & vPrior, vbInformation, "Change"
            vPrior = .Value
        End If
    End With
End Sub
How practical the above approach will be for you will depend largely on frequency of update etc... use of MsgBox purely for sake of demo.

Also, if you're comparing a lot of values simultaneously I would suggest you cache the prior values rather than a multitude of Static variables.
(note: Static variables only persist within session)