Because bc is better at arbitrary precision floating point calculation than bitcoin.
So I stumbled upon a bug in bitclient (a minor bug, obviously) 
I would like to point out that there's no need of an high precision calculator: target is a big number but with few significant digits. The maximum target has only 4 significant hex digits (FFFF), I don't know how many there are in the current target but I suppose there's no need for it to have many more.