Speaking only from my own empirical experience with them, I find the QuasiNewton works the best in the most cases, but there is systems where the FIRE method is better.
The quasi-newton has a major draw-back, that the time it takes to perform the next steps is order N^3 in terms of the number of atoms. So if you are doing a big system with a fast method to calculate the energy and forces, the time spent in the optimizer is the dominant part, so I am doing a classical calculation or doing a neb optimization, I will from time to time use the FIRE.