I've had my Pixel 6 since launch, but just today decided to do a couple side by sides outside with my mirrorless camera. I have a Sony a6400 paired with a Tamron 17-70 f/2.8. This lens is a great comparison because it's widest and longest focal lengths are close matches for the Pixel 6 Pro's regular and telephoto cameras, respectively. To try keep it as fair as possible, I used both in full auto mode and took the images straight out of the body, no manual post-processing in Lightrooom (which I would normally do for images from my Sony). I did, however, downscale the Sony images to 12.5 MP, since the Pixel is giving us 12.5 MP images from its 50/48MP sensors, so this seems to make it more fair in comparing detail rather than leaving the Sony ones at 24 MP.
In the wide shots, there's a much bigger difference. At a normal viewing size, the Pixel details holds up well and looks solid, as does the Sony. However, as you zoom in, the Pixel's image can look fairly over-sharpened and its detail falls apart faster compared to the Sony. There's also a lot of difference in color and lighting. The Pixel does not have any areas where the detail is blown out, unlike the Sony, thanks to the auto-hdr. However the downside to that is that it makes the overall image a lot flatter and you lose a sense of the lighting. You'd almost think I took them under different weather conditions. The Pixel went quite a bit cooler on colors than the Sony and the colors definitely don't feel as rich, though it could be argued the Sony is pushing the color a little too much. Overall, though, I can easily say the Sony image is quite a bit better, but the Pixel is still quite good.
The telephoto comparison is where I was really blown away by the Pixel. I really thought this would fair worse having the smaller sensor and narrower aperture, but wow, did it really hold its own against the Sony. Like, I'm floored how close it gets. Now, of course, this is in bright conditions, but still impressive. In this case, the two ended up with more similar color temperatures than the wide images. The Pixel's image keeps up with the detail of the Sony until you really, really, really pixel-peep. I didn't find it to look as over-sharpened as the Pixel's wide image did, either. Aside from the slight bokeh that you get from the Sony, even stepped down to f/4.5, these images don't look all that different, especially at normal viewing sizes.
Of course, these are also in fairly ideal lighting conditions and the larger sensor in the Sony will help more and more as you get into lower light situations, though Google does a lot of heavy lifting with its image processing to compensate. The Sony also has the advantage of being able to use a whole range of focal lengths, while you are stuck with 3 on the P6 Pro. I do lean heavily on 35mm and 50mm (APS-C) focal lengths when taking pictures on my Sony, neither of which has an equivalent on the P6 without relying on image scaling. All things being equal, I'd always prefer to have my a6400 available for a picture, but I'm glad that the Pixel 6 holds its own as well as it does, given that I don't haul my a6400 around with me everywhere.
(In order, Pixel main sensor, Sony 17mm, Pixel telephoto, Sony 70mm)