ATI Asus 5870v2 or 5850?

Your best bet is to measure the available space in the chassis. Remember to allow around 5cm over the length for the PCIe power connectors that will attach to the end of the card.
The Asus V2 is the shortest 5870 I think (9.5" / 24cm), the other card you linked to is a reference card, and all reference cards are 11" /28cm in length. There are slightly shorter cards on the market (HIS iCooler V 10.7" / 27cm for example) but not significantly shorter.
 
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