I use both NiMH and Alkaline. NiMH for long run times and constant brightness. Alkaline for the "brightness wow factor".
If you like the "wow factor" of brightness that lasts for a short period of time with fresh alkalines then try NiZn (Nickel-Zinc) rechargeable AA cells. It delivers 1.6 Volts. Use caution, there are reports that fresh off the charger the voltage is much higher and could damage electronics; so let the NiZn cells rest before using. Also some users complain about the capacity being low compared to NiMH.
While the "brightness wow factor" is really cool, it is more practical to have a consistent useable level of brightness for a longer duration (until the battery runs down) as with the use of NiMH AA cells. Good for long night hikes, emergency lighting, and you can see when cycling.
For Eneloop, the NiMH cell runs twice as long as generic Alkaline AA and the voltage stays above 1.2V until the NiMH AA is almost depleted. See the 500mA graph for on the Sanyo Eneloop NiMH page
http://www.eneloop.info/home/performance-details/capacity.html. Staying above 1.2V for the duration of the NiMH charge (at constant current) is the key to the consistent brightness factor. Notice how the Alkaline cell drops almost linearly in Voltage over time which results in the light dimming over time until it dies. (If you have a voltage regulated LED light for constant brightness then the NiMH cell has more capacity than an Alkaline AA).
For my Planet Bike Blaze 2W LED lamp, the manufacturer rating is 5 hours on high setting (about 100 lumens) for two Excell Alkaline AA's. With brand new Lenmar R2U (ready to go) 2150 mAh NiMH AA's the run time was 3.5 hours one night plus another 10 continuous hours next day before the two NiMH AA's were below 1.1V.
Years ago, I received 1st generation rechargeable AAA Alkalines by Pure Energy for a gift. I use those to power my Petzl headlamp (40 lumens) which has a low current draw so capacity is not a big issue. I top off the batteries often to get that "brightness wow factor". Otherwise for long trips, I use brand name AAA Alkalines. I prefer Low Self Discharge NiMH AAA's, but I use what I have on-hand.