There are several important cases where it is proved that $\rho(G)<\rho(J)$, with $G$ and $J$ the iteration matrices associated to the Gauss-Seidel and Jacobi methods. See for instance my book *Matrices. GTM 216, Springer-Verlag*. For instance, in the tridiagonal case, $\rho(G)=\rho(J)^2$ thus G-S is twice faster as Jacobi.

What means *twice faster* (or just $k$-times faster) ? These are order one methods, in the sense that a fixed number of exact digits are gained at each step. This number is $\tau=-\log_{10}\rho$. A method is twice faster than an other if the ratio $\tau_{one}/\tau_{other}$ equals $2$. Thus you should see a significant difference between both methods. If not, there might be two reasons. Either you are in an exceptional case where $\rho(G)=\rho(J)$, or something is wrong in your code.

In general, I do not recommend Jacobi and G-S. They are good examples in a course to beginners. But a slight change of G-S yields the relaxation method. With an optimal parameter, it is much faster. This is because $\rho(G)$ is very close to $1$ when $n$ is large, and thus $\tau$ is very small.