You might have to re-calibrate both monitors. What happens when you revert back to defaults on both monitors? Problem still there or does it get better?
When I move the Photoshop window with the photo the way that it spawns across both screens, there is a obvious color difference
This in itself is expected. Photoshop can only convert to one profile at a time. What happens when displaying in a color managed app like Photoshop, is a full profile conversion from document profile to display profile. These converted RGB values are sent to the display.
So Photoshop uses the profile for the display the image is on. When dragging the image over, PS uses that profile until it passes the half-way point over on the other, then it changes profile when you drop it.
That said, it's always a possibility that Windows isn't loading the correct profile for each display. This isn't a common problem, but it happens. You can check the default profile for each display under Control Panel > Color Management > Devices.
Thank you for all your replies. I am following up on the thread on Luminous Landscape, URL above.