I am a bit rusty on my BJT circuit analysis and relooking at my college notes I can't remember the cross-over point when you switch between large signal and small signal models.
The large signal model is just a diode between base and emitter with a current source between collector and emitter whose equation is β.Ib.
The small signal model is the T or PI model where there is the AC dynamic resistance of the diode re between base and emitter and a current source again β.Ib although this can be replaced with a voltage controlled current source gm.vbe where vbe is the small signal voltage across the base and emitter.
Now when you design the bias of the circuit you use the large signal model. When you look at the gain of your circuit you use the small signal model. However when you come to the analysis for instance of a push-pull amplifier I have seen texts use the large signal model and sometimes consider re although it will be negligible at high currents (re = 25mV/Ic(mA)). I just want to get it set in stone in my head so I have a design procedure approach for all situations and trying to remember all this from 30 years ago :-)