Windows monitor calibration is not good enough.
For serious work you need a colorimeter like a Spyder or alike to calibrate your screen.
Do you have GPU acceleration turned on? Any difference if turned off?
Yeah the colour switched back and forward as you switch the gpu on and off.
I very much doubt that the monitor calibration is out. I've never had any problems with prints or viewing onb other displays etc it started with the installation of LR6
I'd keep the GPU acceleration turned off. You're not the first to see this. Adobe is working on improving this.
Also make sure to use the latest AMD graphics diver: http://support.amd.com/en-us/kb-articles/Pages/latest-catalyst-windows-beta.aspx
With the HD6800, I guess the benefits of GPU acceleration are not that big, if any.
I've got 15.8 (beta) running just now and it does make the develop module a bit snappier actually. But disabling the feature doesn't seem like a permanent solution - just a temp workaround.
I tried to contact Adobe directly about this to see if they are actually 'working on it' or not but just got directed to the forums
15.8 is fine since they also have the LR fixes baked in.
If you wish to see consistent and accurate color across applications then you need to do what F.McLion said above. Use a hardware device to calibrate and profile your monitor.
To test this go into control panel settings and change your monitor profile to sRGB as the default and see how the color should match between the modules.
This is not a fix since the color would not necessarily be accurate. You will still need to use a hardware device to develop proper profile.
See this thread.