By default, photo booth save videos in
/Users/UserName/Pictures/Photo\ Booth\ Library
Is there a way to change this default path?
I am on OSX 10.11.5
I report here as an answer my comment above.
You can move the
Photo Booth Library to the location you prefer, this procedure should automatically change the path of the Photo Booth application.
Note that the library is a package that keeps all the photos and the content of the application, if you delete it you will lose all your pics and data.