Which circuit is better for low-noise, high-precision light sensing?
The first one (transimpedance amplifier) will have a much better high frequency response. If you want to reduce the high frequency response you can add a parallel capacitor across the feedback resistor. 

The second will have frequency response limited by the photodiode capacitance. 

Here is a TI application note on calculating noise in a transimpedance amplifier. 

In the second case, you'll have an amplifier with voltage and current noise spectra and Johnson-Nyquist noise in the resistor. 

There is also shot noise in the photodiode.