The thing is, if you want to move to a specific area, there's not necessarily much choice of homes to move to, so I wouldn't strictly judge a style of structure as an indicator of class, unless I saw new owners install pebble dash or faux Tudor cladding or something inappropriate for the building.
But an interior certainly can be a class indicator as it displays personal taste and that in turn shows their exposure to culture and wordly experience.
I live in the cheapest house in my area and I often look wistfully at bigger houses in my neighborhood, quite often I think it's a shame they can afford a big nice detached house with an in out drive, but their front garden looks like a shit tip.