One significant difference is of course that in Germany universities are free, so the overall financial burden of education is not nearly as high as in the U.S. If you stay away from the expensive cities (Munich, Hamburg) or their centers and live in outskirts or other cities with good universities like Berlin or Leipzig, rents are not really that expensive. I paid 150€ / month for a small central room in a shared apartment in a German university town, which I could pay for completely with a student assistantship. Most rents for rooms in shared flats are in the range 200€ - 450€ (depending on the area).

Btw, BAFöG has been such a successful model for Germany that one wishes every country would introduce such a system.