Test this and report on speed please: 
Sub checkdifferences2()
Dim LastRevRow As Long, LastAlphaRow As Long, i As Long, j As Long
Dim RangeToUpdate As Range, SourceRng As Range, RevRngToColour As Range, AlphaRngToColour As Range

LastRevRow = Sheets("Reversion").Cells(Rows.Count, "B").End(xlUp).Row
LastAlphaRow = Sheets("Alpha").Cells(Rows.Count, "B").End(xlUp).Row

Set RangeToUpdate = Sheets("Reversion").Range("F2:F" & LastRevRow)
Set SourceRng = Sheets("Alpha").Range("F2:F" & LastAlphaRow)

RevPO = Sheets("Reversion").Range("B2:B" & LastRevRow).Value
AlphaPO = Sheets("Alpha").Range("B2:B" & LastAlphaRow).Value
RevAD = RangeToUpdate.Value
AlphaAD = SourceRng.Value

For i = 1 To UBound(RevPO)
  For j = 1 To UBound(AlphaPO)
    If RevPO(i, 1) = AlphaPO(j, 1) And RevAD(i, 1) <> AlphaAD(j, 1) Then
      RevAD(i, 1) = AlphaAD(j, 1)
      If RevRngToColour Is Nothing Then Set RevRngToColour = RangeToUpdate.Cells(i) Else Set RevRngToColour = Union(RevRngToColour, RangeToUpdate.Cells(i)) 
      If AlphaRngToColour Is Nothing Then Set AlphaRngToColour = SourceRng.Cells(j) Else Set AlphaRngToColour = Union(AlphaRngToColour, SourceRng.Cells(j))
    End If
  Next j
Next i
If Not RevRngToColour Is Nothing Then
  RangeToUpdate.Value = RevAD
  RevRngToColour.Interior.Color = vbYellow
  AlphaRngToColour.Interior.Color = vbYellow
End If
End Sub
If you want to change what's coloured and how, or want to remove it altogether, come back.