I believe you mean 'Pros' and 'Cons'.

anyway,
I personally don't really like light infantry until rifles become vailable, and I say that for 2 reasons:

1. They are only half the size of normal units. This means that if they get in either a melee or a shooting match with any normal sized units, they will lose.

2. They don't have too much higher of a range than normal line infantry. Because of this and slow reloading times, they might get off 1 shot at a marching enemy before that enemy (assuming they are standard 70-range line infantry) is able to fire back. So, combining that with the half size, and the fact that at a distance of 90 (feet? metres?) most of the rounds wil miss anyway, you end up with only a couple men dead, and a ton still advancing at you.

However, I have also used them to great effect in several examples:

They are a great city garrison for a well-controlled, easily protected city where the enemy will not attack. especially in Crimea or Russia.

If you aer fighting an all- or mostly- cavalry army, light infantry is what you want to use; can deploy stakes mid-battle, have a bit longer range than line infantry, and cavalry + stakes + current A.I.= lots of dead horses. This happened with an insurrection in Crimea once:

So I have 5 units of light infantry (extremely low upkeep BTW) and a howitzer when a rebellion pops up. "no biggy, they probably just used a ton of melee cavalry", well I was right. So, I advanced in a pentagonal formation, with the howitzers in the center. Once I get in arty range, I open fire on the enemy. obviously doesn't do much, but it makes them attack me.
So, I move up a little more, place stakes, and wait. After a litle more 'enticement' from my arty, they finally charged. They might as well have charged over a cliff. massacre and a very short melee ensued, in which i lost a couple men. after the army routed, i moved on to take the general, who routed after my arty bombarded him.

So yes, Light inf. have their uses, but they are very limited.

I suppose using a couple on the flanks to fire at the enemy while they are engaged with your line isn't a bad idea, but with certain formations it's difficult to do (namely the shallow 'V' formation)