You cannot drive an OC high without an external component (simplest being a resistor, but often a relay) pulled to a positive voltage (usually Vcc of your circuit). The advantage of OC is that the external supply can be much higher than the supply voltage of the main circuit. The disadvantage is speed as the resistor has to charge any parasitic capacitance present on the OC output.
An invertor can still be OC but usually will drive high and low and is much faster.