Performance wise they are similar but at stock speeds the 770 is slightly faster but with the 280x you have more vram. It hurts to say as I only use Nvidia cards but the 280x is the better choice as it has the extra vram.
http://hexus.net/tech/reviews/graphics/61201-amd-radeon-r9-280x-vs-nvidia-geforce-gtx-770-4k/