If the Q had that sensor, everybody would wish it had a 4/3 sensor. And if it had that, people would wish it was APS-C. If it was APS-C, people would wish it was full frame. That's just the nature of things
But the thing is, it's not all about just the sensor size. From what I've seen - and someone can correct me if I'm wrong - the Fujifilm 2/3" sensor just doesn't perform as well as the Canon 1/1.7" sensor or the one that Olympus and Pentax use for the MX-1 and XZ-2 (Sony?). And then there's the lens factor. In Canon-land, it seems like the G15/G16 delivers much sharper, contrasty pictures than the S110/S120, I assume it's the lens because the sensor is supposedly the same.
Also, there's the issue of pixel density. Most 1/2.3" sensors are now putting out 20MP or even more (even if the "true resolution" remains much lower). This adds noise much sooner to the image at lower ISOs, so the difference in performance between a 1/1.7" 12MP sensor and a 1/2.3" 20MP sensor is much, much bigger than it would appear to be, the 1/1.7" sensor delivering much better quality images even up to ISO 800 and acceptable even beyond that. It's incredible how far technology has come! I wonder what will be possible 5 years from now!