We report the discovery of HATS-13b and HATS-14b, two hot-Jupiter transiting planets discovered by the HATSouth survey. The host stars are quite similar to each other (HATS-13: V=13.9 mag, M*=0.96M_{sun}_, R*=0.89R_{sun}_, Teff=5500K, [Fe/H]=0.05; HATS-14: V=13.8mag, M*=0.97M_{sun}_, R*=0.93R_{sun}_, Teff=5350K, [Fe/H]=0.33) and both the planets orbit around them with a period of roughly 3 days and a separation of roughly 0.04 au. However, even though they are irradiated in a similar way, the physical characteristics of the two planets are very different. HATS-13b, with a mass of Mp=0.543M_Jup_ and a radius of Rp=1.212R_Jup_, appears as an inflated planet, while HATS-14b, having a mass of Mp=1.071M_Jup_ and a radius of Rp=1.039R_Jup_, is only slightly larger in radius than Jupiter.