I would usually start with a site such as DPReview.com, look for a review of the more recently released camera, and dig down into the image comparison. These are studio examples with fixed graphics, as seen across the full breadth of the camera. For instance, for the G9.
Unfortunately, that is not for the 9x Mark II, and the SX720 is not in the list of comparables.
You can see the feature-list side-by-side there as well.
I would suspect that between the newer camera (which generally will get the a better sensor than the older more-consumer line), the much larger photosites (the G9XmkII is about the same number of pixels, but spread across an area over five times as large), and the lower-zoom lens with significantly larger max apertures, the G9X should produce significantly cleaner and crisper photos. Add the ability to capture RAW and this will allow you to take post-processing to a new level (if you choose to do so).
That said, spec sheets don't shoot photos, and photographer technique will be a major player here.
From a personal experience perspective, I had a lot of fun with this class of camera, and captured some really great pictures with it. Granted, that was a decade and a change ago, and so of course much less advanced cameras than current, and I've since moved on to larger DSLR bodies. But the level of quality I was able to get with an "enthusiast zoom" camera compared to the more run of the mill point-and-shoots was often - although not always - visible. No guarantee the same is still true today of course, although the DPReview review of the class does seem enthusiastic about what it offers over most straightforward cameras.
That said, I would only move up if there is something you want to improve with your current camera. Are you finding that you can't capture indoor scenes well enough? Are you wanting more manual control over the technical bits of photography? Are you looking for more post-processing latitude? These would all drive me towards the G9. Interestingly, the G9 is also more compact and weighs less, making it a better traveling companion. But you do give up the extreme reach of the 270's zoom, and super-bright scene performance (max shutter speed goes from 1/3200 with the 270 to 1/2000 with the G9). And of course purchase price.