Is the cut-off frequency for each high order butterworth filter the same or different?
The natural resonant frequency of a 2nd order low pass filter will have a pole zero diagram like this: -



If you are unfamiliar with pole-zero diagrams see if this helps: -



If you follow that, then go back to the first diagram and you should realize that the undamped natural resonant frequency (\$\omega_0\$) has a value anywhere on the semi circle and it is the Q of the filter how far round from the jw axis the two poles are. Given that any order of butterworth filter has all its poles on the same semi circle, the answer to your question is: -


  Is the cut-off frequency for each high order butterworth filter the
  same or different?


If you mean the natural resonant frequency then YES!

If you mean the 3dB point of each filter's response on the jw axis (the axis that pertains to "real-life" measurements on a spectrum analyser) then NO!

Butterworth pole-zero diagram: -



The above shows the poles of a 10th order butterworth filter - note that all the poles lie on the same circle and therefore all the individual filters (5 x 2nd order) have the same natural resonant frequency.

Taken from here.