Regulated has little to do with color and brightness. It allows the LED to be used in a wider voltage envelope without heating up when you are charging the battery off of the converter. A few years ago some had issues with the ebay LEDs while on shore power. They would get damaged somehow or more likely the heat would cause the imitation 3M tape to give. The answer to the tape was to use cob style (pillar) and at worse need to swap them out for incandescent while on shore power.
I've had some of my panels running at over 17v without failure. For another member I ran a test by running two in series on a 24v set up. They got hotter but didn't fail. The tape on my panels only contacts the reflectors on the edges but none has fallen. In fact removing one to repair a pigtail was so hard I thought I was going to damage the LED or the fixture. In 3 years I have had two failures out of 30 LEDs, both after a long stretch of washboards. 3 emitters went out on a 120 LED porch light and the pigtail on the panel. Not bad at all considering what I spent on them.