Having been unable to actually visit these sights I must go with what I have seen online in pictures.
From what I can tell Monticello has an organic nature with strong influences from around the time it was constructed. Jefferson designed the main building with the ability to add-on and with a few elements that are uncommon for homes of the time. The grounds at Monticello appear well groomed and to have been planned very effectively against the buildings themselves. A very interesting and classical building of the time.
Like Monticello, Fallingwater uses the landscape to increase its own beauty. That is about all they appear to have in common from the outside. Although Fallingwater was designed about 75 years ago it still holds a contemporary look about it. Simple shapes, stark contrasts, parallels and perpendiculars, interesting materials, and unique environmental usage add to the eye catching allure of this space.
Personally I like Fallingwater the most for several reasons personal to me. First I have always appreciated the movement of water and I dream of designing complex fountains some day for enjoyment. So the water elements of Fallingwater are a bonus. Second I would like to see myself as a contemporary designer who uses some of the same techniques that Wright used in this building, simple details, straight lines, and complex layouts. Lastly I have always appreciated nature and how we can combine it with our society (Great Example) and Fallingwater uses the resources around it perfectly to its form. So with that I choose Fallingwater as my preference.
Photo Credit: (http://faculty.evansville.edu/rl29/art105/sp04/art105-10.html), (http://drinknectar.com/2010/11/17/a-virginia-wine-virgin-no-more/monticello-west-exposure/),