Don't know if this will help, but I had the Geocaching Live app on my WP7 Samsung Focus. I recently upgraded to a Nokia Lumia 920, which is WP8, and re-installed the app on it. As far as I know there is no app from Geocaching Live for WP8. Having said that, when I attempted to install the current version, it installed fine on the phone. Geocaching does not yet list my device, or any other WP8 devices that I know of, so I updated my profile to show my device as a Lumia 900, which is a WP7 device.
I used the Geocaching app today on my 920 to locate a cache with no issues. The "start" (or home) button on Windows phone keeps the app running where you left it. At least this is the case for me today as I was navigating and switching to other functions of the phone, such as the camera. If you use the "back" button, then you are exiting out of whatever app is running and have to start over.
I haven't been at this geocaching hobby very avidly, and only have a few attempts at it, when I've had the time and ambition, so it would be good to hear comments from others who use a Windows smartphone to navigate. Personally, I think I'd prefer to use a handheld GPS because I believe it would be more responsive in areas with little or no cellular coverage. I need to try navigating under such conditions to warrant whether I'll actually buy a handheld GPS or not. For as little as I use it for geocaching, the phone works fine.
What platform are you switching over from? Apple or Android?