You probably need to update your display driver for Windows 8.1.AMD, nVidia and Intel all have display drivers for Windows 8.1. I'm not having any such display issue's on my desktop or notebook. Both have 8.1 and current display driver's for Windows 8.1.
It's not a driver issue as much as an issue with zoom setting in the browser. It would be a driver issue if it effected all browsers but seeing how one browser is effected and the other isn't tells me it's a browser setting. Check Chromes zoom settings to what it is then set FF zoom setting to the same.
https://support.mozilla.org/en-US/kb/font-size-and-zoom-increase-size-of-web-pages
http://windows.microsoft.com/en-us/internet-explorer/ie-accessibilty-options#ie=ie-11
Those 2 screen shot are showing as identical on my end....I can't see a difference between the two. Also I thought this was a metro issue and not a browser or window issue. I would like to see a screen shot of your metro screen and a screen shot of your resolution settings.
Checking your specs for the device I noticed there are a few drivers that have been updated since the device was released. In-particular your HD4400 graphics driver and your BIOS. I'd update both, especially the BIOS.
https://www.asus.com/Notebooks_Ultrabooks/ASUS_ZENBOOK_UX302LA/HelpDesk_Download/
There are four sizes you can select for the Metro screen apps from the right click menu, but yours look like mine also.