There are many more ways to solve unstructured dense system of equations (to vary a well-known title, probably at least 19 different ways).
In particular, CGS and BiCGStab are interesting iterative ones, and QR is a very important direct one - numerically more stable than LU with column pivoting.
Comparisons are moot, as advantagens and disatvantages depend on the accuracy wanted, the level of robustness required, and (in randomized tests) the distribution of the matrix entries assumed. It also depends on the implementation (LU comes in different pivoting variants), whether the matrices are appropriately scaled, etc..
Vanilla GMRES is trivially convergent, as after $n$ steps, it minimizes over the full space. (If you limit memory, then you have lots of different GMRES's, and comparisons are even more questionable.)
For superlinear convergence under certain conditions, see
The defining paper ''QMR: a quasi-minimal residual method for non-Hermitian linear systems'' on QMR gives in Section 6 a convergence analysis, again under certain conditions.