I have 3 armlets so far, but I can't really tell what they do.
The armlet of the Sun increases my attack power... Does it give me more damage? How much more? I haven't noticed any difference yet, except maybe the fact that my attacks are blocked less?
The armlet of the Moon increases my defense. How? Do I take less damage? Can I block more attacks?
The armlet of Benevolence I understand. Apparently it gives me 20% more gold, or at least that's what a certain FAQ claimed.
It's hard to tell how much extra damage the Armlet of Sun does, but I'm guessing about 20% more. Same goes with the Armlet of the Moon. If you want to buy an armlet but don't have a lot of cash, I would go for the Armlet of the Sun. I find that it'll generally kill enemies by one less hit (i.e. instead of 5 hits to kill, it'll take four). I don't think the Armlet of the Moon allows you to block more attacks, you just take less damage when you're hit.
When you start playing for karma points (like in the Master Ninja Tournament), the Armlet of the Sun is important, as it lets you kill enemies faster.