We examine transonic diode pumped alkali laser (DPAL) devices as a simpler alternative to supersonic devices, suggested by B.D. Barmashenko and S. Rosenwaks [Appl. Phys. Lett. 102, 141108 (2013)], where complex hardware, including supersonic nozzle, diffuser and high power mechanical pump, is required for continuous closed cycle operation. Three-dimensional computational fluid dynamics modeling of transonic (Mach number M ~0.9) Cs and K DPALs, taking into account the kinetic processes in the lasing medium is reported. The performance of these lasers is compared with that of supersonic (M ~2.5) and subsonic (M ~0.2) DPALs. For Cs DPAL the maximum achievable power of transonic device is lower than that of supersonic, with the same resonator and Cs density at the laser section inlet, by only ~3% implying that supersonic operation mode has only small advantage over transonic. On the other hand, for subsonic laser the maximum power is by 7% lower than in transonic, showing larger advantage of transonic over subsonic operation mode. The power achieved in supersonic and transonic K DPALs is higher than in subsonic by ~80% and ~20%, respectively, showing a considerable advantage of supersonic device over transonic and of transonic over subsonic.