I think the Paraguay river is not the best way to split Paraguay, but rather the Sierras. The Sierras split Paraguay in two different economical and cultural areas to this day. The East is richer, agriculture-based and Brazilian-influenced; the West is poorer, livestock-based and Argentinian-influenced. EDIT: The East was totally covered by the Alto Parana Atlantic forest until 1970, while the West was already covered by livestock ranchs and the whole of the Paraguayan population. END OF EDIT.
So, I think the basin of the Alto Parana should go to Brazil, and the basin of the Paraguay River should go to Argentina.