For $15 I would definitely say the ATi, I just got the HD2900XT 1GB, It's an absolute monster, real power hungry tho. The 3870 Rocks, Ati's third best card.
Eh, get a few less frames with AA with the HD3870 compared to the 9600GT.
All in all, I am into gaming, but I like the other HD possibilities that the HD3870 posses over the 9600GT.