They both do a different job. The batter head produces primarily the energy that is being transformed into sound. It influences attack, volume and tone spectrum. It is also in charge of rebound and of course durability (important when it gets heavy).

The resonant head does exactly what it says on the tin – it resonates. The resonant head amplifies certain frequencies that were produced in the first place by batter head and drum shell. It works a bit like an equalizer. If you put very thin resonant heads on toms they start to sing. The tuning of the resonant head has a big impact on the overall sound of the drum.

The minimal setup for a drum shell is just one batter head – obviously on the top. This is sometimes done in studio in order to place the microphones inside the shell.