The signal-to-noise ratio (SNR) of piezoresistive transducers based on carbon nanotube field effect transistors (CNFETs) is an essential yet unexplored performance metric. Here, we show that the SNR of CNFET piezoresistors made of small band gap semiconducting SWNTs (SGS-SWNTs) depends strongly on the gate bias voltage. The SNR is found by combining low frequency 1/f noise with the piezoresistive signal. We find that SGS-CNFET piezoresistors are best operated at device off-state, where strain resolution is maximal.