amc7135 ground-sinks 350mA, give or take a few tens of milliAmps. low dropout voltage, and it's on the ground-side of the load. Only usable with a single Li-Ion, though some have taken it over the 6V max by heatsinking the chip, and others speculate that you can drop the Vcc with diodes while keeping the supply to the load still high. Doesn't need external components unless LED is more than 2 inches away from the driver.
LM317 regulates voltage, but can be rewired to regulate current. Not just at a constant 350mA, but at a range of currents. Has much higher dropout voltage, though, so need more voltage for it to work. Also needs more external components, like resistors and capacitors.
7135's are the easiest to work with, but if you want to be able to set the current to anything, not just multiples of 350mA, then go for the lm317.