There are a number of useful tid-bits on the topic at the forum thread below...
Saber Forum | General Chat | Technical | Li-Ion battery technology vs. "old school" batteries (Alkaline, Ni-Mh, Ni-Cad)
It probably would have been easier to just post the link. lol.
The main difference, from what I understand(besides the chemical composition, voltage, and all that fun stuff.), is that the Li-ion don't lose voltage as you use power. In other words, they don't start to die slowly like other batteries, they just die when the battery is completely drained. This has it's pros and cons. The main pro is that your saber won't start to dim and your color start to change(if an RGB color), like with regular batteries. The main con is, you have to keep track of when you last charged them, how long they usually last, and how much you use your saber cause there won't be any warning. So it's possible it could go out during a duel if your "math" is off.