We have investigated the temperature and pressure dependence of the threshold current (I-th) of 1.3 mum emitting GaInNAs vertical-cavity surface-emitting lasers (VCSELs) and the equivalent edge-emitting laser (EEL) devices employing the same active region. Our measurements show that the VCSEL devices have the peak of the gain spectrum on the high-energy side of the cavity mode energy and hence operate over a wide temperature range. They show particularly promising I-th temperature insensitivity in the 250-350 K range. We have then used a theoretical model based on a 10-band k.P Hamiltonian and experimentally determined recombination coefficients from EELs to calculate the pressure and temperature dependency of I-th. The results show good agreement between the model and the experimental data, supporting both the validity of the model and the recombination rate parameters. We also show that for both device types, the super-exponential temperature dependency of I-th at 350 K and above is due largely to Auger recombination.