How do I choose the poles and zeros in order to calculate my TF from input & output data?

I have an input signal (T_input) and an output signal (T_output) as values in vector form (from simulation, not real measured values with noise):

T_input=A.data.Sheet1(978:1080,4);

T_output=A.data.Sheet1(978:1080,2);

data=iddata(T_output,T_input,Ts);

sys_2_1 = tfest(data,2,1); % 2 Poles and 1 zero chosen

sys_4_3 = tfest(data,4,3); % 4 Poles and 3 zeros chosen

So I have generated two transfer functions with the same input and output data but different amount of poles and zeros. When I then take the input signal previously into the transfer functions created, sys_2_1 & sys_4_3, they are not giving me the same shape of the original output signal (T_output).

My question is, how do I create an accurate transfer function with my input and output data? How do you choose the poles and zeros?

I have used the system identifaction toolbox to determine the TF and the same issues goes with this method.

Thanks for your time.

Regards, Ibrahim