Do NOT loop through all cells!! There is a lot of overhead in communications between worksheets and VBA, for both reading and writing. Looping through all cells will be agonizingly slow. I'm talking hours.
Instead, load an entire sheet at once into a Variant array. In Excel 2003, this takes about 2 seconds (and 250 MB of RAM). Then you can loop through it in no time at all.
In Excel 2007 and later, sheets are about 1000 times larger (1048576 rows × 16384 columns = 17 billion cells, compared to 65536 rows × 256 columns = 17 million in Excel 2003). You will run into an "Out of memory" error if you try to load the whole sheet into a Variant; on my machine I can only load 32 million cells at once. So you have to limit yourself to the range you know has actual data in it, or load the sheet bit by bit, e.g. 30 columns at a time.
Option Explicit
Sub test()
Dim varSheetA As Variant
Dim varSheetB As Variant
Dim strRangeToCheck As String
Dim iRow As Long
Dim iCol As Long
strRangeToCheck = "A1:IV65536"
' If you know the data will only be in a smaller range, reduce the size of the ranges above.
Debug.Print Now
varSheetA = Worksheets("Sheet1").Range(strRangeToCheck)
varSheetB = Worksheets("Sheet2").Range(strRangeToCheck) ' or whatever your other sheet is.
Debug.Print Now
For iRow = LBound(varSheetA, 1) To UBound(varSheetA, 1)
For iCol = LBound(varSheetA, 2) To UBound(varSheetA, 2)
If varSheetA(iRow, iCol) = varSheetB(iRow, iCol) Then
' Cells are identical.
' Do nothing.
Else
' Cells are different.
' Code goes here for whatever it is you want to do.
End If
Next iCol
Next iRow
End Sub
To compare to a sheet in a different workbook, open that workbook and get the sheet as follows:
Set wbkA = Workbooks.Open(filename:="C:\MyBook.xls")
Set varSheetA = wbkA.Worksheets("Sheet1") ' or whatever sheet you need