I am trying to find out what is physically more difficult, a standing back tuck (back flip) or a standing front tuck (front flip). If you answer this question, please answer why.

Front is more difficult. From coaching gymnastics and being in gymnastics, with very few exceptions, anything forward is more difficult than backward.

To do a standing back tuck, you jump up and your legs, head, etc. give you momentum to go backward. Plus, the bonus of being able to "spot" your landing. 99% of the time I could easily teach someone to do a back tuck in very little time.

To do a front tuck, you must have far more upward momentum because you do not have your legs' weight to help your rotation. You must keep your head in a neutral position, otherwise you end up on the ground, on your face. You cannot see your landing until the last nanosecond. A standing front tuck is rather difficult to teach and learn.

It's all a matter of physics...

Hope this answers your question.