Why doesn't my cookie recipe work in the US?
I can't tell you exact differences, but it is known that differences do exist. 


US flour is frequently bleached. This is illegal in the EU, I don't know how it is in Israel. 
I don't know what flour your recipes are made for. In the US, "all purpose" flour tends to be closest to German 550 flour, and cake recipes in Europe may have been made with German 405 flour (or the local equivalent) in mind, which has a lower protein content. 
US flour can be made from different cultivars than those used in Europe. The best known difference shouldn't make a difference to your cakes - in North America, they grow a lot of hard winter wheat and make so-called bread flour out of it. But even with soft wheat, which is used for all-purpose flour, there is no reason to use the same cultivars, so they probably differ. 
Israel is hot and arid. Flour absorbs a little bit of humidity from the air during storage, and it is possible that, if you are now living in a more humid area, this "prehydration" differs. I cannot tell you what the exact effect is on the final binding power of the flour, my intuition actually would expect the effect to go in the other direction - but I have seen (I think even researched) in another question on the site the difference when flour is stored at different humidities and it is mathematically significant. 
the growth conditions are different between Israel and the surrounding countries, and the USA. While wheat is a global commodity, I wouldn't be surprised if producers gear their blend towards a binding capacity that is traditionally expected in a locale, else they risk selling flour which gains reputation for "not working". 


All this is only a list of possible causes, but it doesn't help you predict how the dough will differ. Luckily, this is a problem which can easily be addressed empirically. Try just cutting the flour back from your recipes and see what the results are. I would go for  maybe 10% less the first time and then continue in smaller increments in the desired direction. Another potential solution is to switch to pastry flour if you have been using all purpose - but it has lower protein content than 405, so if the result is too loose, you might have to start mixing pastry flour and all purpose flour. 

As a final note, pay attention not to buy self-rising flour (unless your recipe calls for it). It won't lead to the dry results you described, but it will give you other problems.