You need not bother, since you are going with the 660 which is just a little slower than the 7870. The difference is not very big between the two.
The difference lies in few things :
1. Clock Speed
2. GPU Cooling Fans / Heatsinks
3. Connection Ports
4. Some Free Goodies like free games etc.
These are the things the companies use to differentiate the same card from other manufacturers and also from the Reference card that the AMD makes which is the card which is not overclocked, uses a standard heatsink, and everything as orignal. The companies make changes to the GPU in order to make it their own.
I would still go with the 7870 XT because it is stronger than the 660 and it fits your budget perfectly.
It does not fit the budget when he is getting an OS also. And the difference between the 660 and the 7870 is quote low, so there is not much bigger problem going for the 660. It is just like 5 percent slower. Check out the comparision at Anandtech for more info between the two.
I chose the 7870 at the first place because it was fitting in the budget but when you said that you need an OS, then i went for the 660 which has recently got a huge price drop which costed the same as the 7870 a few months ago. But now the 660 which performs slighly lower can be had for much lower price.
With the inclusion of the OS, there is not much change is the performance. Check out the benchmarks between the 660 and 7870 at http://www.anandtech.com/bench/Product/548?vs=660 . It can be clearly seen that the 660 is just a little behind the 7870.