AMD Radeon HD 6770 1GB
AMD Phenom II X4 945 Processor @ 3.00 GHz (stock cooler)
6 GB RAM
1 TB HDD
Dell Studio XPS 7100
The 7870 you list trades blows with the NVidia GTX660, which is a little better than the 650 Boost you list. Also, the cooler on the HIS 7870 is slightly better, which means you could overclock it to get even more performance out of the card.
So, my humble opinion is that you should, out of the two, get the 7870.