Mostly, prices come down to demand and design. Some of the mirrorless cameras are neat little designs, and because of that designer flair, they catch the eye of a lot of photography newbies - also, compactness tends to be a selling feature again for those with less full-on photographic knowledge. The mirrorless cameras are selling well, so the price is appropriately higher until they need to lower it. APS-C cameras can sell well too, but the market is more saturated, with far more bodies, models, and brands int he game, so there have to be some sales, price-leaders, and such to stay competitive or move units.
As for quality - it depends on the cameras you are comparing and the conditions you are shooting in. Generally, the image quality difference in daylight, scenic photography is a draw between any large sensor camera - micro 4:3 or APS-C...most folks would be hard-pressed to notice the difference between shots taken with any of 5 different brands of camera, ranging across APS-C DSLRs, SLTs, mirrorless, and micro 4:3 cameras. Where the gap grows a little is when you introduce low light, and require high ISO. APS-C cameras, at least the better of them today, will do better than micro 4:3 once you get to ISO1600 or higher. There may be some difference at lower ISOs than that, but not real noticeably...but get to the high ISOs and it's fairly clear APS-C's better sensors have a big edge.
The only other factor would be speed, control, and ergonomics - which is up to a person's individual needs. None of the mirrorless cameras on the market can focus as fast, shoot as fast, shoot continuous burst as fast, track focus as well, or offer the same degree of manual control as a DSLR. When looking at them as second bodies, a DSLR user can find much to love with mirrorless cams. When looking as a primary body, a person needs to determine if their needs can be met by the mirrorless cameras, or if they need to look at stepping up to a DSLR.
Within the mirrorless class - the Olympus and Panasonic micro 4:3 models are excellent in daylight and decent at higher ISO to around 1600 - far far better than P&S cameras. The Sony NEX system can do better at high ISO since it's using a full APS-C sensor, making it quite usable to ISO6400, and competitive with better APS-C DSLRs. The Samsung NX system also uses APS-C, but doesn't seem to be using as good a sensor as the Sony, as the higher ISOs aren't as good.
As a DSLR shooter, I finally decided to add one of these mirrorless cameras to my collection as a second body to carry when I've got long lenses on my DSLR - I primarily wanted to capture decent wider and landscape scenics without having to switch lenses, and find that the APS-C sensor mirrorless camera can basically capture equal results as my DSLR in daylight - making it a good companion. It could never replace my DSLR though, due to the small ergnomics, poor balance with larger lenses, lack of optical viewfinder, slower focus and lesser tracking capability, and lesser battery life.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses