The Sony RX100 series is always ranked among the very best compact cameras for image quality - they use the larger 1" sensor...
This is going a bit OT for an, "Inexpensive," P&S, but Sony does tend to be very good at playing to test charts, but if you look at the real world performance of 1" sensors and what's going on, every single 20 MP 1" sensor is made by Sony and is in the same generation - the Nikon J5, RX100 original through the latest, every Canon, Panasonic, Leica, literally everybody. And the color science has been really nailed down to each specific brand's look, with microlenses and the Bayer filter colors tweaked to match nicely to the lens it's paired with.
In short: if it's a 20 MP 1" sensor, it's much of a muchness in the IQ department and the largest difference is going to come down to trademark color and lens design of each manufacturer. See also: battery life is pretty bad on all of them if it's going to be your main shooter, so be sure to pick up an extra.
So how the heck do you pick? Well, I'd stick within your chosen ILC camera brand if you can (sorry Nikon peeps, you shouldn't get the J5 since it's dead, and the DL never arrived) to keep the menus and basic controls as similar as possible, as well as making the aesthetic look very similar for editing. After that, lens specs to make sure it's fast enough and has enough zoom range, and then size for what you're willing to carry (check out camerasize.com for a nifty if buggy comparison tool).
They're not the camera for me since they're too big for too limited of a zoom range to be truly pocketable, or so large I've got a bag and might as well carry an ILC, but my wife loves shooting with 1" and uses it as her good camera so she doesn't have to worry about the compromises picking up one of mine that are tailored to specific situations. Nikon got it right back in 2011: 1" is a wonderful compromise sensor size, clearly better than a phone, and a perfect jack of all trades but master of none.