We had good results on hardhats for our bridge inspectors using the Pelican 2630 LED headlight. The rear mounted battery box (3-AA) helped balance the weight of the lamp and batteries are easy to find.
The lamp comes with two mounting straps, one stretchy cloth for bare headed use and a single rubber strap for hardhats. It worked very well. Different power settings to save battery power.
I use the PT Apex, with some velco straps around the side holes to keep the elastic headband from sliding off the hard hat. The light is on the front of the hat, just above the brim. It can be angled down to shine where you are looking. Be sure to get a headlamp that has adjustable angles.
Most times, the standard LED's are more than adequate. If you need throw, the center LED is great. And the Apex (or EOS) can be upgraded.
The only problem is weight. The Apex gets heavy after several hours of use. The Apex Pro would be lighter, since it's got (2) CR123's, instead of (4) AA's. Either option gives you more brighter light options, and better runtimes than AAA lights.
For my work, I rarely need throw. I also carry a Fenix P3D as my primary light. I'm likely going to get a Zebralight H30 for the hardhat. The weight is insignificant, and can run for days on low. I'll probably use the Zebralight for backpacking too.
I saw that our lights were mentioned here. The Command and Performance are our most popular hard hat lights.
The Command Series Headlamps offer 3 modes and a flashing red rear Safety LED to help be seen. There is the option of 10 or 20 LEDs.
Our Performance headlamps are On/Off only and are slightly brighter and a bit heavier. The Tactical version also comes with a clip that fits in a hard hat slot to help secure the strap and therefore light to the helmet. We also have a version that is Intrinsically Safe:
UL913 Class 1, Div 1 Groups A-D, T6 & UL913 Class 1, Div 2 Groups A-D, T6
Both run on 4 AAs and are available in Fire Resistant and Tactical models.