You can see that the sensor in the G1X has similar performance to that of the 7D.
As DxOMark points out, that's both good and bad.
Good: getting the IQ of a dSLR in a much smaller form factor.
Bad: a newly-designed sensor for a 2012 camera, with the same 4.2µm pixel size as the 7D, performs essentially identically to the 7D, a sensor designed about 2.5 years before the G1X.
That means that either 1) Canon didn't try to improve the pixel characteristics of the sensor, 2) they tried to make it better and failed, or 3) they do have the ability to make it better, but chose not to include those enhancements in the G1X sensor. I think #1 is pretty unlikely. I hope it's not #2, because that bodes poorly for the next generation of APS-C sensors they release. I'd be unsurprised by #3 - in fact, that's very logical if they're going to release a new APS-C sensor (7DII, 70D) soon and want to prempt comments like 'Canon's much cheaper point-and-shoot G1X offers the same IQ as this expensive new dSLR'.