Comment author: @xavierleroy

I agree this is a annoying problem with big_int, but I'm afraid there is no solution: big_int is a mixed Caml/C datatype, with a Caml record encapsulating a sign, a size and a low-level "nat" type implemented in C. The custom comparison functions would have to be attached to the big_int type itself (attaching them to the "nat" type just gives the wrong results), and there is no way to do so in OCaml.

I can only recommend that you replace big_int by Zarith in your code:
http://forge.ocamlcore.org/projects/zarith/
Not only Zarith is faster and more space-efficient than big_int, but it also supports polymorphic comparisons perfectly.