from what i can see form all of the reviews i have seen is that the HD 3870 and 9600gt perform very similar to each other. The cards seem to be mostly tied when gaming without AA (it bounces around lots form game to game) they 9600gt may have a TINY lead without AA and when you turn AA on the lead seems to grow a little bit. but overall they are pretty close.
so lets say performance is the same. it comes down to:
power consumption - relatively the same
heat - i would say 9600gt is a bit cooler
features - the HD3870 does have DX10.1 but that is useless for while. but overall HD3870 wins
overclocking - form what i have seen so far the 9600gt oc's like a mad man (past 830 core i believe) and considering shadder clocks scale higher than the HD3870 i would say the 9600 wins by a small margin
drivers - personally i don't like ATI's drivers and i prefer ntune to CCC overdrive
Multi GPU - again seems to be very similar depending on the game and settings
and finally price - Where i come form (Canada) the 9600gt is cheaper than the HD3870 by a good amount. the 9600gt can be had for $180 were the HD3870 is $200 (after the price drop) and if you go for multi GPU price thats a $40 savings. and $360 for a pair of 9600gt's is far cheaper than $450 for a HD3870X2
this is for Canada not europe and not the US (although they tend to similar) and form what i can tell prices in europe tend to favor ATI cards so in that case the Hd3870 would be the better choice.
for myself i would choose the 9600gt but both cards are good and are very competitive to each other.