Can Xbox 360 display 1920 x 1080 photos at full resolution?

I believe it used to display 1080p photos back in the day, but that got broken in the transition to Metro. Or you don't have your display set up to display images without overscan. The 1080p test pattern here will help you verify your overscan setting and give you something with distinct single-pixel resolution to test with.

http://tigerdave.kicks-ass.net/forum/viewtopic.php?f=19&t=357&sid=e44a5ff76f26b6102d948b9fc26bc346

1080p is only about 2MP. Your average photos will be much larger than that. So Xbox needs to scale it down. Xbox is using a very simplistic scaling down algorithm to scale down photos. As a result, the photos will appear soft and out of focus. To achive good results, a much more complex scaling algorithm needs to be used to preserve the details. But most of these set top boxes (including BD players) don't use it. So to achive best results, you need to use your PC to scale those pictures down as close to 1920x1080 as possible.

It's as if the original post never started out with: "I tried displaying a 1920 x 1080 photo"...

is the Xbox hooked up to the same TV as the PC?

That's a good call

Why would that be a good call? A local PC isn't going to fix the 360's broken picture viewer.

Okay, I took a minute and threw up some test patterns. The 360 definitely scales 1080p still pictures down and then back up for display. I had assumed that it would be to 720p and then back up, but it looks to be even lower. Without spending that much time on it as I don't care that much, it looks like images get scaled down to about 540p internally, then scaled a second time to whatever your chosen output resolution is. So a 1920x1080 image becomes roughly 960x540, then is spit out as mangled 1080p.

This is similar to the way the 360 handles video ever since the Metro dashboard update. Pre-Metro, 1080p video would display as full-resolution 1080p video if you were set to 1080p output. Metro brought with it a known flaw that scales any video down to 720p internally, then scales it a second time to whatever your chosen output is. The exception to this is the Zune Video service, which maintains 1080p throughout. A conspiracy theorist would have you believe that this is malicious and intentional to promote their own video service. Looking throughout the rest of the video lineup at how often black levels and surround audio are accidentally broken, and then subsequently never fixed? It's pretty obvious that it's a matter of incompetence.

In short: Yeah, the picture viewer is broken. It's not just you.