it seems that handing from one balcony to another even above 10 t'fochim across a reshus ho'rabim if it is on the same side of a building is ossur but to parallel builduing is potur bc one is similar to the way the levliyim did it and the other is not. but i don't understand how one is similar and the other is not?
The difference lies in the fact that the wagons (balconies) are always facing the Reshus ha'Rabim, as the wagons were proceeding down the Reshus ha'Rabim. Therefore, in the case of the balconies on the same side of the building, the setup is the same as that of the Agalos, with the length of Reshush ha'Rabim between them.
In the case where one is handing from one balcony across to the other balcony on the other side of the street, this is called handing to the side, as the balconies are viewed as if they are wagons which are continuing to travel down the Reshus ha'Rabim. They are therefore not considered facing each other, but on the side of each other, with the width of Reshus ha'Rabim between them.
All the best,
Yaakov Montrose