Vim is no different from Emacs in that the actual background color can't be changed within overall application window, all the "windows" in Vim must have same background. As dash-tom-bang says, though, the status line can be used to give some visual cue to which window is active. This is done by using the 'highlight' command to set the StatusLine and StatusLineNC highlight groups to have different colors, active window will have status line with color of 'StatusLine' highlight, and all other windows will have the 'No Cursor' StatusLineNC highlight.
There is also the txtfmt plugin, which (despite some misleading screenshots) doesn't really let you have different backgrounds, but it can be useful to give some added diferentiating to windows, a little clunky by requiring you to add marker characters into your text: http://www.txtfmt.webs.com/