I would definitely NOT recommend connecting the LED directly to any power source able to deliver more current than you want in the LED.
The adjustable voltage/current boards are great, but keep in mind that there is always some minimum voltage loss from input to output. In some it can be as little as 0.1V, or it can be as high as 1V or even 2V. This is called the overhead voltage. Once the difference between the supply and the LED is less than the overhead voltage, the output current will start to drop, and the LED will start to dim.
For example, say your LED draws 1.5A at 12V, and your regulator's overhead voltage is 0.5V. When your battery starts out at 12.6V, everything is great. Battery drops to 12.5V, everything is still fine. Battery drops to 12.4V and things start to change. The output voltage can only be driven to 11.9V (12.4V minus the 0.5V overhead). The LED will still work at 11.9V, but it will no longer draw 1.5A and won't be as bright. Battery drops to 12.3V, output goes to 11.8V, LED gets dimmer.
But say you had 1.0V overhead. This would never be able to drive the LED to 12V, and thus not to 1.5A. However if you switched to a 6V, 3A LED, the regulator would happily drive it at full power until the battery dropped to 7V. A good switching regulator could do this with quite good efficiency.