I have mixed thoughts about the X10's noise profile. On one hand, at low ISO sensitivities Fujifilm doesn't overdo it with the luminance noise reduction for JPEGs, so you end up with grainier photos than most, but without the concomitant loss of sharpness. However, it produces an odd aliasing-type artifact on fine details, such as the tape measure, and details like text never really cohere. But at high sensitivities this approach manages to preserve detail a bit longer than luminance smoothing usually allows. That's in the standard manual shooting modes. If you use the EXR High ISO/Low Noise mode, which drops to 6 megapixels, the JPEGs are quite nice up through ISO 400.
These ISO 100 shots comparing the two cameras give you a better sense of the X10's artifacts in the text and on the tape measure. The X10 has a slight advantage over the G12 thanks to the faster lens, which means you don't have to use the higher ISO sensitivities as much.
You can definitely get better results at high ISO sensitivities by processing the raw files, though the odd noise pattern of the sensor requires a different approach to editing the files. I had to bump up luminance noise reduction higher than normal and sharpen, which I usually don't use too much.
These ISO 1600 shots are just to illustrate the differences in the raw noise pattern of the X10 vs. other cameras. The G12 exhibits the typical small "grain" noise, while the X10's noise reminds me of the worm artifact produced by early halftone patterns. Neither is significantly better than the other, but since the X10 differs from the norm it requires different techniques for raw processing.