The dipper I talked to out here in CA only dipped. When I asked him about all the boxed in areas and pinch welds that I wouldn't be able to paint, he didn't have an answer. So I went with media blasting.
That's great that the dippers in your area can protect all the metal afterwards but it would need to be a dip to get inside all the inaccessible areas. Remember that Chrysler dipped these cars in primer at the factory.
My car was on a rotisserie so by the time I was ready for paint, all the media was out.