Macro to compare columns and copy rows.

Option Explicit

Sub DoThings()

    Dim wsN As Worksheet, wsO As Worksheet
    Dim lrow As Integer, nrow As Integer, i As Integer
    Dim str As String, str2 As String
    Dim fndrng As Range
    
    Set wsN = ThisWorkbook.Sheets("NEW")
    Set wsO = ThisWorkbook.Sheets("OLD")
    
    lrow = wsN.Range("A:A").Find(what:="*", searchdirection:=xlPrevious).Row
    nrow = wsO.Range("A:A").Find(what:="*", searchdirection:=xlPrevious).Row + 1
    
    i = 2
    
    Do While i <= lrow
        Set fndrng = wsO.Range("A:A").Find(what:=wsN.Cells(i, 1))
        str = "A" & i & ":F" & i
        
        If fndrng Is Nothing Then
            str2 = "A" & nrow
            nrow = nrow + 1
            
        Else
            str2 = "A" & fndrng.Row
            
        End If
            
        wsN.Range(str).Copy
        wsO.Range(str2).PasteSpecial xlPasteValuesAndNumberFormats
        Application.CutCopyMode = False
        
        'Enable the two rows below if you want to delete the row from New after it has been
        'processed. Remove the ' to un-comment. Also, if you enable them, delete the row below
        'them.
        
'        wsN.Rows(i).Delete
'        lrow = lrow - 1

        i = i + 1   'Delete this if you enable the two commands above
        
    Loop

End Sub