The reality is, most cheaper point and shoots are not better than good camera phones. That's partially just because camera phones have gotten fairly good.
More expensive point & shoots start to add potential higher quality. But, the more expensive the camera gets, the more complex it gets, and they still require a greater expertise to get great pictures.
The RX100 mentioned above (which I recently bought and will be using at Disney tomorrow), is probably the best point & shoot currently on the market. But it's 2-3 times the price of most point & shoots. ($650). And for someone who just quickly points and clicks, it won't necessarily do a that much more than a cheaper camera. But if you want the portability of a compact camera, with the potential of a much bigger camera, then the RX100 is a great camera.
There are several cameras in the $200-$400 range, which take pretty good pictures, and are pretty easy to use. The Canon S95 and S100 are probably the overall best in this price range for pure quality.
Many Point & shoot owners value having super zoom abilities -- The ability to zoom into fine detail from a great distance. The best quality point & shoots, including the 3 listed so far, have limited zoom ability. It's often a trade off between zoom potential and overall picture quality.
The best travel superzoom cameras are probably the Panasonic Lumix and the Sony Cybershot HX20, and Canon SX260.
For camera comparisons, I'd recommend snapsort.com