(looks like Bill Gates types faster than I do!)
Someone more expert than I will likely need to solve this, but I'll try another question.
Assuming you're running dual monitors (MBP display and Asus), in the Display window that lists the resolutions when you open SystemPrefs->Displays go to the Arrangement properties and make sure "Mirror Displays" is unchecked.
You should then have a resolution choice list showing on each display. Does the one on the Asus correctly identify the monitor? Are you selecting "1080p" as your Resolution? There won't be a 1920x1080 choice using HDMI since 1080p is effectively the same thing.