Faster, yes. Use less power is debatable. I would like to see some graphs. Yes the transistor inside a chip is very small, but you have to connect it to other transistors and here things start to get fishy. And when everything is a synthesis library, is even worse. The only real better transistors are in analog ICs.
Faster, maybe? I recall seeing a graph towards the end of the planar transistor days (maybe around 22 nm?) that FO4 speed peaked around 45 nm. Overall clockspeeds continued to improve because of lower power usage and thermal limits, but in isolation a smaller transistor is not necessarily faster; less capacitance and inductance, but also more resistance.