From what I read from Lithium battery makers, they recommend the discharge/recharge method. Also works on revamping your Laptops lithium battery as well. May not get you back to max, but it gains you something. In addition, the phone's charge circuitry slows down charging as it approaches full charge, to a slow trickle charge, especially when the device is on. Charges faster when the device, phone or laptop, is off. Laptop batteries last 45 minutes vs the 2 hours you got when your first got the laptop (also 6 cells are the standard, 8 and higher cells are premium $$). you can do the discharge/charge and gain maybe 20 minutes back.
In addition, batteries, including Lithium laptop batteries, have "plug in" rating. Cell phone batteries are rated for 300-500 plugs-ins (not exact). If you charge it every day you use 1 - so every day charging or 2 times a day diminishes this plug-in lifespan. If you could run the battery down and charge less frequently, you can extend this total lifespan of the battery.