Comparison theorems play an essential role in studying the properties of the fractional equations. Firstly, a comparison theorem for ABR type fractional difference equations is proved. Next, based on the proven comparison theorem, the connections between the solution for an uncertainty fractional difference equation and its $\alpha$-path are established. Then, the uncertainty distribution of solutions for ABR type uncertainty fractional difference equations is also derived. Finally, examples are given to verify the correctness of main results.