I have the Pixel 6 (non-Pro) and the S22 Ultra. It's honestly hard to compare the two because they are so different.
The Pixel is easier to handle day to day because it's smaller. For me it has more personality than the S22 Ultra as well. The hardware design, color (I got the Sorta Seafoam), and quirkiness of Material You is really charming and fun to use. The camera is also really good. And to top it all off it's literally 1/2 the retail price of the S22 Ultra.
The S22 Ultra on the other hand is a beast of a phone that means business. It has every feature I can possibly think of. A huge beautiful display, great camera (from what I've seen so far), the SPen, the boxy design I missed from my Note 20 Ultra, and much better auto brightness. Seriously, the auto brightness on the Pixel 6 is even worse than OnePlus, and that's saying something. There's also all the extra features that Samsung puts on top of Android. It can feel overwhelming if you haven't used a Samsung in a while, but it's worth it imo.
If one wants a fun to use, fairly customizable, super fast at the basics kinda phone the Pixel 6 line is awesome. And to top it all off it's a great value. If one wants a do-it-all device the Ultra is definitely a better choice.