Few observations after a month of use:
Picture quality overall is great, however the stock app tends to overblow the highlights in high contrast scenes. This is the effect of the small sensor size and it's prominent on all cellphones, however both Pixel 2 and iPhone X I've tested don't have that issue. However, installing and using the Google camera port helps the issue dramatically, so it's the HDR algorithm employed in the stock app, not the actual sensor.
Stock camera app is, however, both faster and more reliable in terms of snapping every day photos. Furthermore stock app has marginally less noise than Google Camera, but it also captures marginally less details. Stock camera also has less saturation and sharper gradients than Google Camera, likely a product of the algorithm as well.
The telephoto camera is decidedly worse than the wide angle one, even in bright light. You're trading off the dynamic range for zoom, and it's not just the difference in the lenses.
Lightroom HDR raw files (40mb 3.2MP image that contains 10 bit of colour) are mind-blowing. As an owner of full-frame Canon 6D I was blown away by the colour retention in Lightroom Camera app. On a DSLR you'd absolutely have to use bracketing to get those colours (although you'd get a 20 MP image), it's very impressive that a cellphone can do that. If only it shot out a 12 MP raw file.
Overall Note 8 has a very versatile camera with awesome picture quality, but certain scenes require he use of Google Camera for HDR+ algorithm to get the best results.