Nexus 6P RAW vs JPG*
* Actually Custom vs In-Camera Processing

Although this is a comparison of RAW vs JPG, it's not about the file format. The comparison is really External vs In-Camera image processing:

JPG files from your phone's camera are always processed by the the camera's firmware before being saved. This processing severely degrades the image.

RAW files completely bypass being processed by the camera's firmware, and are a direct representation of what hit the camera's sensor. This means any app can replace the processing normally done in your camera.

So, showing JPGs isn't really about how bad JPG is. It's showing you how bad the phone's camera firmware is. It consistently ruins the image in two ways:
RAW Developed in Lightroom 6.0 (Luminance Noise Reduction OFF, Chroma Noise Reduction 25%)
View mode: A/B Toggle
Switch to Side-by-Side
Click on images to toggle between RAW / JPG
JPG

Outdoors Dusk IV (81 ISO)
This RAW reveals just how much detail the 6P captures before being smudged by default processing. Subtle blue tones in the leaf, cracking, and fine veins all show through very well. Even more impressive is that this crop is from the edge of the frame, where resolution typically falls short.
JPG

Daytime (60 ISO) - JPG 100% Crop
Again, the RAW contains far more detail than I would have ever expected from a phone. The built-in processing (JPG) completely mangles the image and destroys all of that detail. I'm beginning to feel really bad for camera engineers who work on phones -- they build a device that punches way above its weight, only to have it all destroyed by the in-camera software.
JPG

Cloudy II (85 ISO) - JPG 100% Crop
Complete garbage in the JPG: the trees in the background have become a mush. Their red-brown leaves are muddy gray. The backhoe's yellow-orange is muddy gray. I don't understand why noise reduction is even used here! The RAW noise level is already low.
JPG

Lime (198 ISO) - JPG 100% Crop
A 100% crop of a lime. These don't even look like they were taken with the same camera.
JPG

Cactus Flower (67 ISO) - JPG 100% Crop
A very small (~5mm or 1/4") flower. The texture of the leaves is completely different in the JPG.
JPG

Cat. (243 ISO) - JPG 100% Crop
RAW: Cat; JPG: Worse cat.
JPG

Bricks (660 ISO) - JPG 100% Crop
The default noise reduction algorithm has no idea what to think of bricks.
JPG

Office wall, spotlight. (144 ISO) - JPG 100% Crop
The JPG has completely blown out highlights, total loss of details in the bright areas, and strong blotching / oversharpening in the background.
JPG

Cameras (167 ISO) - JPG 100% Crop
In the JPG: big changes to metallic surfaces; the out-of-focus areas are oversharpened. Everything is oversharpened.
JPG

Sand Toy (60 ISO) - JPG 100% Crop
A macro shot of this sand toy shows built-in noise removal annihilating sparkly bits of sand.
JPG

Cloudy (60 ISO) - JPG 100% Crop
Low-contrast outdoor scene.
JPG

Outdoors Dusk (60 ISO) - JPG 100% Crop
More of the same.
JPG

Outdoors Dusk II (69 ISO) - JPG 100% Crop
The default processing (JPG) tends to make everything look like watercolor. Hopefully everybody prefers that to actual detail.
JPG

Outdoors Dusk III (85 ISO) - JPG 100% Crop
While the default JPG seems to completely ruin colors of overexposed areas (yellows), these colors are well preserved in the RAW file.
JPG

Cloudy II Overexposed (Uncorrected) (85 ISO) - JPG 100% Crop
There appears to be aggressive highlight clipping in the default JPG's clouds, but not in the RAW file. Below we'll see if that's true by reducing the exposure 4x (or -2 EV).
JPG

Cloudy II Overexposed (-2 EV) (85 ISO) - JPG 100% Crop
Reducing the exposure by 4x shows that the RAW contains far more dynamic range than the default JPG, which harshly clipped the bright areas in the clouds, destroying detail.
JPG

Indoors, Average Lighting (100 ISO) - JPG 100% Crop (Nexus 5X)
An indoor shot of average brightness. The default JPG has applied aggressive noise reduction and then sharpened everything, resulting in smudges with halos. The greens in the plant are gone, too.
JPG

Mostly Darkness (1348 ISO) - JPG 50% Crop
A very dark outdoor shot at a moderately high ISO. While the RAW file appears very noisy, it still contains far more detail than the default JPG. Does anybody prefer the JPG? Why is the default processing so afraid of noise?
JPG

Mostly Darkness II (1348 ISO) - JPG 100% Crop
Same situation as above. The RAW contains more noise, but also contains more detail, color, and intensity range. We can easily see the vague tree line against the night sky.
JPG

Mostly Darkness III (1088 ISO) - JPG 17% Crop
Even across the whole image, RAW files look better. This is scaled down to 17% of its original size, but the RAW file still shows better color, more detail in the shadows, and no 'crunchy' watercolor effect. It does start to show some strong blue tinting in the shadows, though.
JPG

Very Dark Indoors, Overexposed (1892 ISO) - JPG 67% Crop
Very dark indoor scene of a dim (~25W) light, overexposed. They're both pretty bad, but the default in-camera processing wanted every detail in the JPG to die.
JPG

Medium-Lit Indoors (60 ISO) - JPG 100% Crop
Some potted plants against a dark window. In-camera processing seems to really hate leaves. It also made the pots look like playdough. Cool?
JPG

Overexposure Correction (Uncorrected) (494 ISO) - JPG 33% Crop
Indoor shot slightly overexposed. Pay attention to the color of the wood on the cabinet, and the intensity gradient on the bottom white thing (convection oven). The next image lowers the exposure 8x (-3 EV)
JPG

Overexposure Correction (-3 EV) (494 ISO) - JPG 33% Crop
With an 8x (-3 EV) lower exposure, the color of the cabinet's wood grain stays true in the RAW, but turns a strange yellow-green in the default JPG. The bottom white thing also shows stronger highlight clipping.
JPG

Overexposure Correction II (-3 EV) (494 ISO) - JPG 40% Crop
Same image, different place, again with the exposure reduced 8x (-3 EV). The default JPG's oven mitts have completely clipped to white, and we get no more detail out of the countertop's texture. Although the RAW file gives us some room in the highlights, it's not very pleasant ... but I'll take it.
JPG

Underexposure Correction (Uncorrected) (1348 ISO) - JPG 30% Crop
A severely underexposed outdoor night image at moderately high ISO. The RAW file shows more noise as usual (who cares?), but also shows more detail. Let's see what we can get if we adjust the exposure up by 4x (+2 EV) below.
JPG

Underexposure Correction (+2 EV) (1348 ISO) - JPG 30% Crop
Increasing the exposure 4x (+2 EV): ouch. There is absolutely no more detail to be had in the shadows of the default JPG. Although the RAW file looks unusably noisy, it manages to reveal detail that wasn't visible before. The garage door's windows are much more clear, the strip along the roof is well defined, etc. You can actually identify the roof shingles.
JPG

Extreme Darkness (3762 ISO) - JPG 100% Crop
An extremely high ISO night shot in near total darkness. Some 'real' cameras even struggle with noise at more than 3200 ISO. The RAW is ridiculously noisy, but does anyone really prefer the default JPG's smudges? One looks like film grain, the other looks like a disaster.