LLLT for hair loss. What is the difference between LEDs and Laser Diodes?

I won't reiterate what others have said before except to emphasize that consumer purchased devices will have lower power as compared to professional units.  However, the key to these therapies is consistency.  One must use them routinely to see benefits and often it is hard to develop a routine that incorporates these treatments.  Also, as others have said, combination treatments with PRP, rogaine, or finesteride  will show the best results.  

Red light therapy or low level therapy has shown promise in decreasing shedding and even promoting growth by the augmentated vascularity associated with treatment. 
Typically patients will follow protocols several weeks in duration after which it can take a few months to see results. I have found it to be most helpful as an adjunct therapy used in conjunction with other modalities such as medical therapy, topicals and PRP.With regards to your specific question, most home therapies will be weaker than professional grade offerings. LED are lower strength than laser but mitigate this through scalp contact delivery. The main advantage of a home device is convenience.
As always, discuss your concerns with a board certified plastic surgeon (ABPS) with experience in hair restoration.
Donovan Rosas MD
Board Certified by the American Board of Plastic Surgery
Member: American Society for Aesthetic Plastic Surgery, American Society of Plastic Surgeons
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Low level light therapy has been clinically proven to help with hair growth and there are a few FDA cleared devices available. LED light or laser light can be used to deliver the photons to the scalp. The professional devices are stronger and will deliver a higher does to energy to penetrate through the skin and hair. Home devices have the advantage of being able to physically touch the scalp and may offset the lower energy and you have more access to it so that you are likely to use it more frequently. The wave length that has been shown to be effective in growing hair is the mid 600nm range. LED tends to be less costly than the laser devices and it is unclear at this point whether one is better than the other. Either way, be sure to purchase a device that is FDA cleared for hair growth. Cheap LED devices that are nothing more than fancy Christmas lights can be found on the internet and they do nothing but waste your time and money. LLLT works best in combination with other treatments such as nutritional support (We like Nutrafol®) and other treatments such as minoxidil or finasteride. LLLT also helps boost the effects of PRP injections. All of these treatments alone or in combination will help thicken thinning hair but they will not grow hair where the follicles no longer exists. For advanced male pattern baldness, hair transplantation with the FUE technique is the best option. 

A laser diode is a semiconductor device in which a diode is pumped directly with electrical current and converts electrical energy into light.  An LED is a light emitting diode.  Both produce light energy. The amount of voltage determines the power of the light and some are built to handle a higher voltage.