This kind of ad-hoc task tends to be best solved by a generic automation framework to provide basic building blocks (e.g. commands to retrieve window geometries and move windows around), with a small script that implements your specific requirement.
On Windows, AutoHotkey is a general-purpose desktop automation scripting environment for Windows. It's open source. The scripting language makes Basic look not so bad, but it gets the job done.
Here's a script which switches the position of two windows. It works the way you describe: click on one window, switch to another window, and these two windows will be transposed. The script binds the action to the keyboard shortcut Ctrl+Alt+F; change the
^!f:: line to pick the hotkey you prefer. After installing AutoHotkey, save this script to a file called
flip-windows.ahk (the name isn't significant, only the extension is) and add it to your startup scripts (or run it once to test; there's an icon in the task bar with an exit command).
;; Switch the position and size of the active window with the one immediately after in
;; top-to-bottom z-order.
;; This action is bound to the hotkey Ctrl+Alt+F.
;; Bind the action to Ctrl+Alt+F
;; Set id1 to the window ID of the active window
WinGet, id1, ID, A
;; Set id2 to the window ID of the next active window (the one that Alt+Tab would
;; switch to). To do this, iterate over the active windows in top-to-bottom order.
;; This order is: first permanently-raised windows, then the active window, then
;; the next active window.
WinGet, ids, List
current := ids%A_Index%
IfNotEqual, current, %id1%, Continue
next_index := A_Index + 1
id2 := ids%next_index%
;; Retrieve the coordinates of the two windows
WinGetPos, x1, y1, w1, h1, ahk_id %id1%
WinGetPos, x2, y2, w2, h2, ahk_id %id2%
;WinGetTitle title1, ahk_id %id1%
;WinGetTitle title2, ahk_id %id2%
;MsgBox %id1% "%title1%" %w1%x%h1%+%x1%+%y1% <-> %id2% "%title2%" %w2%x%h2%+%x2%+%y2%
;; Move the two windows to each other's coordinates
WinMove, ahk_id %id1%, , %x2%, %y2%, %w2%, %h2%
WinMove, ahk_id %id2%, , %x1%, %y1%, %w1%, %h1%
If you just want to send a window to another monitor, Windows 7 has this built-in (Win+Shift+Left, Win+Shift+Right), but if that's not exactly what you want you may be able to build something better with AHK (some sample AHK scripts may inspire you, e.g. 1).