LED flash uses a lower voltage to work, thereby ensuring a longer battery life. It can be made to fit very thin smartphones and it is cheaper to manufacture and install. Unfortunately, LED flashes are not very bright, leading to lower image quality.
Xenon flash is of a higher technology. It offers a a brighter light than LED. This ensures clearer images even at night. Xenon can be bulky and makes the device bulky. They don't fit in thin smartphones. They also consume a lot of battery power. They are mostly used in real cameras, not camera phones.
Dual-LEDs are simply 2 LED flashes on one phone. It is meant to correct the shortcomings of the single LED flash, by providing more brightness.
Xenon is the best but also the most expensive.