I don't have an ultra but I do have an s22 plus. I also have the Pixel 7 Pro. Between the two I use the Pixel now almost excellent and I don't miss the Samsung or it's gimmick features.
Everyone has a different opinion and use case. The s pen is an advantage in certain situations if you don't have a tablet and need to sign legal documents. Otherwise on a small screen I don't see any real use for it.
The edge panels and Dex are things I will never use because I have other devices that fill in the gap.
I really hate all the bloatware on Samsung devices since time immemorial. Apps that you can't disable or uninstall, 3rd party apps preinstalled and of course the numerous duplicate apps. Then there is Bixby. Completely unnecessary and useless but you don't have a choice to get rid of it.
Despite all of the hate I have towards those things I like Samsung and the integration between PC, tablet, phone and watch. Very similar to Apple. I like Samsung back ups. I like some Samsung apps. I like the hardware on Samsung probably the best of any Android device out there.
So I am always torn on Samsung devices.
Considering the price of the Pixel 7 Pro and features it has everything I need and nothing I don't. Sure, there are a few Google apps I could live without but in general it is as close to software perfection that you can get on Android. Although the hardware is not as good as the Ultra it is really good for the cost. I also like the direction Google is taking with Tensor. Less about maximum performance that most phones throttle anyway and more about sustained performance and AI.
I have felt the 7 Pro is really good in terms of stability and reliability compared to previous Pixels which is a huge factor for me. The cameras are some of the best, certainly the best I have used on a smartphone, the screen is calibrated perfectly and just an absolute pleasure. The battery life is good enough and performance has been seamless. The UI and animations super smooth and pleasing. The modem to my surprise has been excellent.
I got this phone on sale and at less than the cost of the regular s22 MSRP it is simply hard to beat. Add Pixel exclusive features and feature updates and fast updates and it is one of the best phones out there.
Samsung s23 ultra will have better hardware for sure but does that translate into a better user experience is something only each of us can decide. I too, am extremely tempted by the s23 ultra but the cost of that phone is pretty crazy to me. Almost double what I paid for my Pixel 7 Pro and I can say with certainty that it is not double the phone!