We present GaAs/AlGaAs double quantum well devices that can operate as both electron-hole (e-h) and hole-hole (h-h) bilayers, with separating barriers as narrow as 5 nm or 7.5 nm. With such narrow barriers, in the h-h configuration we observe signs of magnetic-field-induced exciton condensation in the quantum Hall bilayer regime. In the same devices we can study the zero-magnetic-field e-h and h-h bilayer states using Coulomb drag. Very strong e-h Coulomb drag resistivity (up to 10% of the single layer resistivity) is observed at liquid helium temperatures, but no definite signs of exciton condensation are seen in this case. Self-consistent calculations of the electron and hole wavefunctions show this might be because the average interlayer separation is larger in the e-h case than the h-h case.