You can do it by using an event macro that looks for changes.  But this can
easily break if the user doesn't allow macros to run--or even turns off events.

I wouldn't use this.  I'd allow the user to update a single cell and use a
formula in the other cell to retrieve the value.  I think that technique is
safer.

But if you want to try...

This code goes behind the ThisWorkbook Module.

Option Explicit
Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
   Dim OtherSheetName As String
   
   If Intersect(Sh.Range("a1"), Target) Is Nothing Then
       Exit Sub
   End If
   
   If LCase(Sh.Name) = "sheet1" Then
       OtherSheetName = "sheet2"
   Else
       OtherSheetName = "sheet1"
   End If
   
   On Error GoTo ErrHandler:
   
   Application.EnableEvents = False
   Me.Worksheets(OtherSheetName).Range("a1").Value = Sh.Range("a1").Value
   
ErrHandler:
   Application.EnableEvents = True
   
End Sub