Why would you choose Gauss Jordan over Gauss seidel numeric methods?

Answer 1

It will solve the solution "exactly", but will take a very very long time for large matrices.

Gauss Jordan method will require O(n^3) multiplication/divisions and O(n^3) additions and subtractions.

Gauss seidel in reality you may not know when you have reached a solution. So, you may have to define the difference between succesive iterations as a tolerance for error. But, most of the time GS is much prefured in cases of large matrices.