I also picked the x3400 over the Sony 1080, but for different reasons
I'm sure the OP has made his purchase by now, but in the interest of contributing to the knowledge base I'm going to share my experience with having had both of these receivers set up in my home within the past week. I ended up choosing the 3400, but for none of the reasons others mentioned.
First, in terms of sound quality the Sony gives up surprisingly little to the Denon, especially for HT. The difference in sound is minimal. I'd give the Denon the nod, but only barely, they both sound great. In fact, I was able to get the Sony sound to my liking faster than I could with the Denon and with less tweaking. If they were the same price and this was your only consideration, I'd pick the Denon, but the difference in audio quality does not seem worth the difference in retail price if that's what you're paying.
Second, I think the DCAC vs Audyssey is also overblown. Both got the distance to my speakers pretty close, and both had some quirks. DCAC labeled my front speakers "large" and therefore had no crossover (I manually switched them to "small" and 80hz crossover); Audyssey set my crossover to 40hz and set my sub to -12db (I manually upped crossover to 80hz and boosted the sub by 6db ... for now ... I may add more). After those and several other recommended tweaks both were sounding great. I preferred Audyssey, but again, the end result is so similar that it also doesn't seem worth the difference in price (in my opinion, having just worked with both).
Both got warm. The Sony got a little warmer, but neither seemed "too hot."
The deciding factor for me was the clunkiness of the Sony's interface and use. Several options had noticeable lag to them. When I turned on the Sony I stared at a "no input" screen for 10 seconds. Worse, the Sony would then revert me to the home screen where I had to select the activity, then another screen to select the source, then finally I could watch TV. There's a 40 page thread on it here with various "workarounds." In the end, the inability to simply push a button and watch TV was the dealbreaker for me. Because of other less tech savvy people in my house also using this system the multiple remote, multiple button push thing was not an option. I didn't want to buy a mid priced receiver and have to "work around" inherent shortcomings.