The THG review shows the 9600GT to be the better card for a little more money.
http://www.tomshardware.com/reviews/best-graphics-card,2404-2.html
With the small difference, finding a good sale on either can weight the balance. Alternatively, and perhaps better, look at the charts and pick the one that does better on the games YOU play.
Does your budget PC have a large enough PSU to support the upgrade? These cards don't take too much, but some budget PCs have small PSUs.