There is a lot of confusion on this topic.
The approximately $200 a month is correct. That is what is referred to as “datot”. That is what the government gives married men who are learning full time in kollel. Not one penny more. Kollelim that pay more are doing so with funds that the roshei kollel raise privately, and that have nothing to do with the government.
There is something else called “kitzvat yeladim”. This has nothing to do with being chareidi. It is an across-the-board monthly stipend that goes up according to the number of children the family has. It is not major money, but it helps. A family with 8 children gets about 1850 NIS per month, which is about $425-$450.
Obviously, chareidi families on the whole get more kitzvat yeladim than their secular counterparts, because they have more children. This stipend only goes up to age 18, by the way, meaning that for every child who turns 18, the stipend gets reduced.
Then there are tax breaks. These also apply equally, based on income and the number of children. There are income tax breaks, and then municipal tax breaks. These, too, have nothing to do with chareidim.
Is it true that chareidim pay less income tax than the rest of the population? Yes, obviously, because our income bracket is much lower and our birthrate is much higher. Any chiloni family is welcome to make the same income and have the same amount of children, and they will get the exact same tax break.