At high ISO test done by dpinterface.com Canon G1 X showing a significantly less amount of noise than the Canon EOS 7D DSLR, Canon G1X comes with a 2.5 inch sensor and canon 7D sensor is approx 27% larger than the Canon G1 X, both cameras are almost even in terms of pixel density.
Lens used on the Canon 7D was the Canon EF 24-70 mm f2.8L USM, Images displayed below are JPEGs out of the camera, not RAW.
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Canon G1 X vs. Nikon V1 vs. Panasonic GX1
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