Interesting question! I had fun doing some searching of my own, and I think I can piece together a decent theory.
Using this site as a main source, it looks like after the initial patent in 1867, there were many different designs patented and sold by many different companies.
I'm sure that some designs work better than others for different purposes, but what this really says to me is that it's more about who has the rights to manufacture and sell a particular design.
According to that museum site, the "Ideal paper clip/clamp" was patented in 1902 by the Cushman & Denison Mfg. Co.
I think it mostly comes down to personal preference between competing designs.
Edit: to try to address what advantages the design might have over others, here is what this site claims in its marketing:
Butterfly shape Designed to minimize paper tearing Large, No. 1 size clamps hold up to 150 sheets
Butterfly clamps are designed to hold large, bulky papers securely. Butterfly design protects against tearing or paper. Heavily tinned steel wire offers excellent rust-resistance. Wire ends are located safely in the corners of clamp.