My now old compact camera died of a lens failure, so I'm in the market for a replacement. What I'd do if I were looking for a new SLR/mirrorless-esque camera would be to go and read the thorough reviews all over the web and make an informed decision - but that level of detail just doesn't exist for the cheaper end of the market.
However, one thing which is pretty much true for the interchangeable lens cameras is that there's not really a significant difference the image quality from similar cameras by different manufacturers - the entry level model from Canon will produce pretty much the same images as the entry level model from Nikon, Pentax, Sony or anyone else, and this hasn't really changed for a good few years. Does the same thing apply to small sensor cameras, in which case the answer is pretty much "buy whatever I can get the best deal on" or are there non-trivial differences between the image quality of similar cameras from different manufacturers?
Note 1: I'm not looking for recommendations of which camera to buy - that's off-topic here.
Note 2: I'm well aware that the image quality from small sensor cameras isn't going to match up to that from an SLR. I own an SLR and use it - but sometimes it's too big to carry around. I'm looking for something really small here, but which does better than my phone.