Compared to the Canon PowerShot G12
While the G1 X may initially appear to be a G12 with a slightly lumpier lens on the front, putting them side-by-side makes clear that Canon hasn't quite achieved the impossible: it hasn't fitted a sensor six times larger into the same body size. However, it's done a great job of minimizing the difference. With the lens retracted, the G1 X is 5mm wider and 17mm thicker than the already brick-like G12. Note though that the G1 X has a narrower lens range, that extends only to 112mm-equivalent (as opposed to the G12's 140mm equivalent).
The G12 isn't exactly the smallest of compacts, and the expansion required to accommodate that larger sensor (and the larger lens it requires) have made the G1 X still less portable - although it'll still just about fit into a large jacket or coat pocket. However, for a camera with such a large sensor, useful lens range and a viewfinder, there's little to touch it.
G-series PowerShots have never exactly been 'small' cameras but this doesn't seem to have harmed their popularity. If you visit any major tourist destinations, it's unusual not to encounter a good number of G-series cameras in the hands or around the necks of holidaying sightseers. If people are happy to carry around a camera this size, we'd assume that they'd willingly accept a slight increase in size and weight, if it came with a substantial image quality improvement.
Compared to the Panasonic Lumix DMC-GX1
Here's the G1 X alongside its anagrammatic interchangeable-lens competitor, Panasonic's Lumix DMC-GX1 fitted with the tiny X 14-42mm F3.5-5.6 OIS powerzoom. The Lumix GX1 offers interchangeable lenses, but the Canon G1 X has a larger sensor, longer lens range, optical viewfinder, and articulated LCD.
The G1 X is rather taller than the Lumix GX1, due substantially to its built-in optical finder, but is only marginally thicker despite its longer zoom range and articulated LCD. Of course the GX1 only 'wins' here due to its unique pancake powerzoom - no other kit zoom for mirrorless systems comes close to this degree of compactness.