I picked up an Asus 770
over holiday sales for $300 after a $10 rebate, and I'm very happy with it. But I probably wouldn't buy it for its currently listed price of $360 after $10 rebate.
I'd say it comes down to which vendor-specific perks seem more compelling to you. When prices are not being gouged, the 280X provides a bit more performance per dollar than the 770 and the future potential gains of Mantle, whatever those might be. The 770 gets you G-sync to use with all these fancy monitors being announced at CES
(edit: Just heard about FreeSync - NVIDIA might not have the G-Sync advantage for long). And GameStream if you think you might get a Shield. I was surprised with a Shield as a Christmas present - though I was skeptical at first, it's turned out to be a really cool little device.
However, all bets are off currently--the pricing landscape at the moment is scary and confusing and just much too high.