Hmmm. I would definitely, no doubt go for the HD 6870. Though if you care about heat and noise like crazy, then the R7 260X would be a better choice. But there is not a very big difference between the two graphics cards when it comes to heat and noise. But when it comes to gaming performance, the HD 6870 would blow the R7 260X out of the water. In the end it's a sacrifice between heat and noise or performance. If you ask me, I would totally sacrifice heat and noise for performance in this case.
Best of luck. Hope I helped.