How do I find out if a program uses GTK 2 or 3?

Use ldd. Mine appears to use gtk2 libraries.

$ ldd /usr/bin/inkscape | grep gtk
    libgtkmm-2.4.so.1 => /usr/lib/x86_64-linux-gnu/libgtkmm-2.4.so.1 (0x00007fa8de4d5000)
    libgtkspell.so.0 => /usr/lib/libgtkspell.so.0 (0x00007fa8dcfe1000)
    libgtk-x11-2.0.so.0 => /usr/lib/x86_64-linux-gnu/libgtk-x11-2.0.so.0 (0x00007fa8dc9a7000)

Inkscape currently uses GTK2. Inkscape trunk has the ability to compile against GTK3, however that is a work-in-progress and is far less compact than when built against GTK2 (GTK3 was created with touchscreen support in mind, so widgets are larger).

-an Inkscape dev