> Then, it should be considerably faster

Why would you expect that? Both algorithms involve a number of (bigint) operations that's proportional to log(p), so it's going to be down to the constants involved and the running times of the individual operations. Is there a clear reason for your expectation that the xgcd-based algorithm should be faster?

Remember that Python has a subquadratic multiplication (via Karatsuba), but its division algorithm has quadratic running time.