I spent the last year using a Pixel and still have it, I now use the Note 8 and really don't notice much difference between the two. The Pixel may have been a little faster but not in anything I'd notice day to day. As far as lag goes, I've had none. When I first got the Note 8 I went through my library and installed EVERYTHING that had an install button. I had 10- 15 launchers, many camera apps, tons of photo apps, all the games I had previously installed that hadn't been sunset, over 300 apps. It filled the phone up to 47gb without any personal content. Even after turning on all the assistance apps and device administrator permissions I still didn't notice any lag outside of when I opened a file type for the first time and it had to build the gigantic list of possible apps for me to choose which one I wanted to use. Even then I wouldn't call that lag, that's expected processing time. I ran that way for over a month before I just got tired of scrolling through an endless list of apps to find the one I wanted. But even during all that, I still managed 7hrs of screen on time, compared to just 4.5 on my Pixel with less than half of those apps installed. Last week I performed a factory reset and other than having a smaller list of apps, it feels the same as having hundreds of apps installed with multiple overlay apps. LMT, Pie Control, etc.
The one major difference between the two phones for me is the camera. I really liked the Pixel camera. I can use the ported gcam and it gives similar results but I can't tie it to a quick launch button like the stock Note camera.