Colloidal GaAs quantum wires with diameters of 5-11 nm and narrow diameter distributions (standard deviation = 12-21% of the mean diameter) are grown by two methods based on the solution-liquid-solid (SLS) mechanism. Resolved excitonic absorption features arising from GaAs quantum wires are detected, allowing extraction of the size-dependent effective band gaps of the wires. The results allow the first systematic comparison of the size dependences of the effective band gaps in corresponding sets of semiconductor quantum wires and quantum wells. The GaAs quantum wire and well band gaps scale according to the prediction of a simple effective-mass-approximation, particle-in-a-box (EMA-PIB) model, which estimates the kinetic confinement energies of electron-hole pairs in quantum nanostructures of different shapes and confinement dimensionalities.