Gojo in One Piece

When Luffy was 7 years old, he ate the Gomu Gomu no Mi in the original story. Now, what would happen had Shanks brought a different fruit, and how would that change the story?

The Limitless Fruit, also knows as Mugen Mugen no Mi (both Limitless and Infinite translate to Mugen) is a fruit that's very special. It can qualify as all three types of Devil fruits, Paramecia, Logia and Zoan, as it does many things. Paramecia for one, since it grants the user a "superhuman" level of information gathering. Logia, because it brings something known as "Infinity" between the user and everything, and because of it's special abilities. Zoan, because it grants the user a change in appearance and grants boosted physical abilities. For one, it grants the user the "Six Eyes Technique", which allows one to gather an extreme amount of information quickly. Second, it grants, well, a change in appearance. You get white hair.

What would happen if Luffy's Gomu Gomu no Mi was exchanged for the Mugen Mugen no Mi? What difference would it make?