I posted a few weeks ago about ordering a Pixel 4, and how I justified it, so I won't rehash that here. Let me just talk about the phone.
The phone is the same size as the 2, or pretty close, but the screen is larger. It has a reasonable bezel at the top with a speaker and the various sensors, a thin bezel at the bottom, and rounder screen corners. I personally think all of the notch and bezel opinions are silly, and I don't care that there's technically more screen real estate. As long as it properly fills a 16:9 ratio when horizontal, it truly doesn't matter.
I think the back is actually glass now, but the white one at least has this really great textured feel that doesn't get finger printy. The sides are a nice black composite material, and the power button is orange. Mostly none of that matters, since I immediately put it in a rubber-like case, as I've been doing with phones since 2012-ish. It also helps protect the camera bump, which is now a square.
The biggest change is the switch to face unlocking instead of the fingerprint. It generally works, but sometimes it feels a half-second too slow, and I'm not sure what the criteria is for it to "look" at you. Is this an improvement? I think it's just a lateral move. The fingerprint was at least intentional, where sometimes you just want to look at the time on the phone or a notification without unlocking it. I'm on the fence, which is to say in the long run I probably won't care either way.
The phone initially defaulted to gesture navigation, which I think was available already in the newest Android on my previous phone, but I didn't know. Basically it means that side swipes acted as the back button, bottom swipes were like pressing home, and swiping up half-way and stopping was like the task switching button. I tried it for a few days, and it felt slower. With this elongated screen, I can say for sure that I definitely don't need that screen real estate for apps. I switched it back to the old school buttons.
From a capability standpoint, I do notice switching apps is slightly faster, and they're also more likely to maintain state, presumably because of the RAM availability. But also, if what I remember about Android is correct, this is more about how developers implement state when the app is closed, forcibly or otherwise, so I wouldn't blame that on Google either way. The crazy high 90Hz refresh rate is sometimes obvious in scrolling, but mostly in animations inside of apps, especially games. It's a subtle usability tweak.
The radar is pretty cool. It is one of the things that instigates the face scanning, which made unlocking a little awkward in the Bahamas last weekend, where the radar is not authorized for use (because it's radio frequency energy). It was slower to unlock in those cases. Where I suspect most people will dig it is that you can wave your hand over the phone to snooze an alarm. You can "air swipe" to the next song, but I haven't tried that. It's a neat hardware trick, but I think it's just another sensor to add to the suite of gyroscopes and such.
The camera is, as you would expect, extraordinary. It delivers on everything they talked about in the announcement. White balance is improved, low-light photos are impossibly good, and the portrait mode has definitely improved, especially with hair. The computational zoom is probably an improvement, but it isn't perfect, and I think some of the gain in image quality comes from having a second camera. Is it better than the Pixel 2? Yes, incrementally. Comparing photos of the two, I think the biggest thing is that the white balance is more accurate in a variety of light sources. It also manages to squeeze out a little more dynamic range in those difficult scenarios.
Is it worth $800? No, I don't think any camera is. If it weren't for the Fi credits and trade-in, I'd never pay that much when a $500 phone is almost as good. Heck, the $200 Motorola I got my mom is pretty great. I'm paying for the opportunity to be at the front of the camera technology, mostly, and if I was more budget conscious, I would likely be satisfied with a less expensive phone.