To add to Stephan's answer, I have tried both packages when solving puzzles from "Euler project":
* "bigints" is pure Nim and has the best API in my opinion, but it is about twice slower than "bignum" and has some issues (see comments in source); it is still a work in progress. * "bignum" uses the "gmp" wrapper and frequently uses types as "clong" in its API which I don't like. But it works fine with good performance. Curiously, I have found Python (using "pypy" interpreter) to be more performing when dealing with long integers than Nim with "bignum" (for instance when doing Rabbin-Miller primality tests). So, it seems there is still room for some improvement.