The Gtx 760 is a better bet of the two, the 760 is comparatively newer architecture (270/270X are basically better 7870's). If you have the budget go for the 760, but either ways both are great cards for their prices.
and yes having a better cooled case can improve performance, but if you can I suggest get the Asus DCUII card.
One last thing, with Nvidia, their new cards overclock yeilding greater results but only when the card is running cooler, so get a card with an after market cooling. AMD will run stable anyways so based on your budget and PC case go for whichever suits you.