This is a tough decision that I recently had to make, and I went with the R9 280X. I kept an eye out for sales, and I paid $299.99 for the HiS R9 280X Turbo Boost edition, which is around the market price of what a R9 280X should be.
I've only had it a couple days, so I can't give a full review, but I am happy with my purchase. The R9 280X were not shipped with reference coolers at all, I believe, so noise should not really be an issue. With a decent vendor-cooling solution, heat isn't an issue either - mine hardly goes above 60C when gaming, and that is with the 1050mhz boost.
Performance aside, the two big deciding factors for me that tilted me towards the R9 280X was the extra RAM, and Mantle. People will argue that Mantle is niche, but in the games it supports, it will help my AMD-based rig. More games will support it in the future. If DirectX happens to expand on this concept in the future - good! Still no loss for me.
As for some of the other minor features that are nice, like video-recording software and easy game optimization, those can be treated as equal. Nvidia may have the convenience of having Shadowplay and game-optimization under one program, but using MSI Afterburner and AMD/raptr's "Gaming Evolved" isn't too much different. (Admittingly, I don't care for raptr.)
All this said, pick whichever one you're willing to pay for. Both are great products. The R9 280X may be better for your AMD-based rig, though.