As in other federal countries, it makes sense to elect one purely by popular vote, the other by giving each state equal representation.
To pass a law, you'd then need 50% of people and 50% of states to support it.
This is a simpler system for elections, and keeps the power of people and states more balanced.
e.g. Germany uses a very similar system (Bundestag being elected by popular vote, Bundesrat being chosen by each state).