In Windows 7 there was the one of my favorite features for wide screen monitor - ability to snap one application to left side of the window, and another to right by moving window title to left or right, now it snaps only to small part of the screen, so for example to do comparison of two browser windows is not possible. Does Windows 8 still have ability to snap window to half of the screen?
Yes, but only in Desktop. Snap in Desktop behaves more or less the same as in Windows 7.
You can't open two browser windows in Modern UI anyway.
Simply drag the window (within Desktop) to the side of Desktop (easier when it is full screen, thanks @JourneymanGeek), as you would do in Windows 7:
It's also possible to use the side Snap for Modern UI (e.g. for chatting) at the same time as Desktop taking up the majority of the space with its own Snapping: