Display omitted •PBE and LDA agree in predicting the thermal conductivity of III-V semiconductors.•PBE predicts a smaller acoustic-optical phonon gap than LDA.•This leads to softer force constants but increases the number of scattering events.•BAs is a limit case due to its extremely large acoustic-optical gap. In this contribution we assess the performance of two different exchange-correlation functionals in the first-principles prediction of the lattice thermal conductivity of bulk semiconductors, namely the local density approximation (LDA) and the Perdew-Burke-Ernzerhof implementation of the generalized gradient approximation (GGA). Both functionals are shown to give results in good agreement with experimental measurements. Such a consistency between the two functionals may seem a bit surprising, as the LDA is known to overbind and the GGA to soften the interatomic bonds. Such features ought to greatly affect the value of the system interatomic force constants (IFCs) which are necessary for the first-principles prediction of the lattice thermal conductivity. We choose AlAs and BAs to represent III-V semiconductors in the zincblende structure. We show that, in the case of AlAs, the errors introduced by the approximate exchange-correlation functionals tend to cancel themselves. In the case of LDA, the overbinding generates larger absolute third-order IFCs, which tend to increase the three-phonon scattering rates. On the other hand, larger absolute second-order IFCs lead to a larger acoustic-optical phonon band gap which in turns decrease the available phase space for three-phonon scattering, compensating the increase in the scattering rates due to stiffer IFCs. As AlAs is a typical III-V semiconductor in the zincblende structure, we expect these findings to hold for general compounds of the same family. On the other hand, BAs can be considered a special instance thereof: due to the large gap between acoustic and optical phonons, the available scattering volume for three-phonon processes is already very limited in both LDA and PBE. In this case we find that the LDA increase in scattering rates due to stiffer bonds is partially compensated by an increase in phonon group velocities.