Every movie has some scary/intense scenes. We own all the movies mentioned above and some of them my kids find scary (The Lion King recently sent my 5 year old into hysterics FWIW) and some they don't find scary at all.
Of all of them, I think that The Aristocats, Lady and the Tramp and Cinderella are the least scary.
Just FYI, Peter Pan is pretty racist by modern standards. The Aristocats has its moments as well.
ETA: If you thought Tangled was intense, IMO The Lion King is FAR more intense.
Beth, mom to older DD (8/01) and younger DD (10/06) and always missing Leah (4/22 - 5/1/05)