NiZns recharge around twice as fast as Sanyo Eneloops, but last maybe 75% as long and require a different charger.
See this discussion thread.
If you use your flashes continuously in a short amount of time, a higher capacity NiMh will actually perform better than a Low-Self-Discharge NiMh like eneloop. If you don't intend to discharge the batteries in a shorter period of time, they will begin to self-discharge and LSD has the advantage. Here are some recent test numbers I found for non-NiZn:
Alkaline: 4.0 sec. min. recycle time; 110 min number of flashes
Lithium: 4.5 sec. min. recycle time; 230 min. number of flashes
NiMh (non-LSD 2600mAh): 2.3 sec. min. recycle time; 190 min. number of flashes
NiMh (LSD eneloop): 2.3 sec. min. recycle time; 165 min. number of flashes
This older chart in a Nikon flash manual is in agreement:
Here are two videos, one comparing NiMh vs NiZn and the other NiMh with battery pack vs NiZn:
Reportedly, it makes an even bigger difference with flashes older than that 580 EX II
With NiMH, a smart independent channel charger is essential for best performance. Otherwise you are overcharging and undercharging certain cells, leading to greater wear and worse performance.