My wife has an 8x and I have the 822. I really like both and our intention was to swap, but now I'm not sure I want to. Here is what I see as the pros-cons:
Ergonomics: 822's buttons are easier to press and better located (with the power on the side). 822 feels better in the hand with the round corners, though HTC feels very sleek. I worry more about dropping the 8x. 8x takes up less room in pants pockets, which for guys is kind of important. HTC definitely feels more premium and sleek but 822 has that 'just right' feel and everything is just solid and pleasant. I think I prefer the wider/shorter aspect ratio of the 822 for things like typing in portrait mode. You have a decent amount more space per key to type on that way.
Feature differences: Battery and expandable memory is a personal preference. Only you know if this is important to you, though being able to ADD 64GB to 822 is a very comforting option! I was surprised to enjoy the Nokia exclusive apps as much as I do. I had that ranked as one of the lowest things, but it's actually a solid difference and maybe the biggest reason I wouldn't swap with an 8x. Hate that there are exclusive apps though, hope that trend doesn't continue because it is obvious that Nokia is putting a ton of software people into WP8 development and HTC probably never will. I want HTC to succeed too!
Cameras: I did do a few side-by-sides and 8x is a bit better. Not a huge difference, if you want 'great' shots, you should be using a dedicated camera anyway. The front wide-angle camera of the htc is really good, I thought it would be just good for skyping, but self-portraits are way better now. We were at a football game and took a shot of us; you can see the entire section fan out behind us and it's a pretty decent picture.
Screens: Last but not least. Yes the 8x screen is better in that it is incredibly sharp but it is the blander of the two. AMOLED screens (822) just pop with color to the point where things almost seem cartoonish. I kind of like this, especially with WP8. The colors are more saturated and brighter and the blacks are deeper. There have been several times when I looked at the exact same thing on both phones. It is hard to tell the difference. If you really try, you can tell that text is a bit sharper on 8x and photos just look a bit better. But that?s side by side and trying to see differences. I read A LOT on my phone and have heard all this hullaballoo about 'retina' displays and how you just can't go back to lower resolutions?. I thought it would be the same for the 8x, that I just wouldn't be able to look at the 822 after the shear ecstasy of reading such crisp text on the HTC?. Nope. I'd probably prefer the HTC screen but the difference to me isn't NEARLY what I tend to read from reviews.
Gorilla Glass: This surprised me. I like to use my phones 'naked', the way they were designed to be used, especially one like the 8x. So after a few years my phones will have a few scuffs and dings but the screen is generally perfect because it's really hard to scratch gorilla glass. The 8x screen had a scratch in it days after it was new. So either there is a flaw in their process or the raised-glass design causes the screen to take more direct attacks when laying on it's face or in the pocket (which would be ironic considering one of the very few htc 'exclusive' features is the face-down-silent trick). Though I prefer the raised glass design of the 8x and the 920, this might be a disadvantage in screen durability compared to the old-school flat-in-body glass of the 822.
Sound: I was listening to an NFL radio game broadcast on Sunday. The app is horribly glitchy (just like on Android) but it's the only way to listen to live action this side of Directv Sunday ticket. So because the POS app kept crashing and otherwise misbehaving, I switched between the phones several times. I was surprised at how much better the HTC external speaker sounded. Radio football broadcasts sound pretty bad anyway, but on htc it was good, on 822 it sounded way more harsh.