Don't know about "richer" but South is definitely more developed than much of the North, especially the Gangetic belt.
Southern states have better HDIs, better social indices, higher total literacy, higher female literacy, better general hygiene, higher percentage of school going children, higher per capita income, greater GDP (except Gods own country), lesser infant mortality, lower TFR, better infrastructure and better industrialisation. East of NCR, North and East are industrial graveyards (like the Gods own country), gets worse the more East you go.
Heck just look at most Southern leaders/CMs compared to those of the North and East and look at their contributions to their respective states.