Most important for great photos is the sensor size and lens quality.
I agree that the Canon and Nikon lenses are the best for entry models, they produce nice soft fading with the Nikon producing a slightly better bokeh but that’s a matter of taste. Nowadays there are also entry model cameras with Zeiss lenses and even some affordable ones with a Leica lens which are of course a class better. For example the Sony RX100 has a large sensor + a Zeiss lens making it the best overall compact camera currently available.
Another option, if you have roomy pockets or don’t mind carrying it in a separate bag/purse and want to obtain professional photographs is a system camera such as a Lumix with a f/1.7 20mm pancake lens.