Simply open two (or more) windows simultaneously, resizing them appropriately, with the two (or more) websites displayed separately in each of them.
You've not said which browser you're using but pressing Ctrl and N together in Firefox (and probably in most other browsers too) opens a new window. Click the overlapping squares in the top right corner to make the window size flexible and then drag the edges so that it takes up half the screen. (Click-and-drag near the top of the window to move it about). Repeat for your original Window and then load the websites into the different windows.
To be honest though, I'd find it just as easy to open the site in separate tabs and then flick between them.