Our homes have changed over the last 70 years, including homes size, building technology, family size, and a rise in standard of living. As people's income increased over the 20th century they bought bigger and better homes. This caused the median home value to go up even when taking into account the effect of inflation. For example a full bath cost a lot since you need double plumbing for hot and cold water while a flush toilet needs a home connected to a sewer system or septic tank. In addition, housing costs include both land and the house; where building space in limited (i.e. cities) land will increase in value with population growth. Median home value calculated by the U.S. Census factors in all of these changes and covers the housing markets in both rural and urban areas. While the historical price index created by Robert Shiller looks at home prices as an investment (like stocks) focusing on the resale prices of a subset of the standard, unchanged houses in large metro areas.
Data Source for Housing Price Index from Robert Shiller's Irrational Exuberance Median Home Values: Historical Census of Housing Tables Home Values; "An Approach for Calculating Reliable State and National House Price Statistics" Characteristics: Housing Characteristics In The U.S.; Median and Average Square Feet of Floor Area