Common Base Amplifier - Hybrid-Pi vs. T Model
Without the equations you get it's hard to know exactly what's going on, but you wouldn't expect to get a "gm" term when you solve for the gain T model, as the model consists of a current controlled current source Beta*ib in series with the dynamic emitter resistance.  The two are related, however, as Beta*ib = (Beta/r_pi)*v_pi = gm*v_pi.  For the T model of a common base amplifier with source resistance Rs and load resistance RL, one should get the gain as being (alpha*RL)/(Rs + Re), with Re being the dynamic emitter resistance.