I would say Dune first but give Hyperion a shot. I actually just finished the Hyperion cantos the other day and am still working through the 6th Dune book.

I personally think Hyperion has some cool ideas and concepts but just never really hit greatness for me.

To also mimic what others are saying Dune changes drastically after book 3 and 4 and Hyperion is basically separate stories split between books 1,2 and 3,4.