The R9 290 is faster and has more memory. It also includes Mantle support and is usually cheaper.
The GTX 780 uses less power and produces less heat. Noise depends on the cooler used, but generally these are quieter.
The GTX 780 also has Nvidia only features like ShadowPlay, g-sync and PhysX.
The choice largely depends on the features you want.
There are also new Nvidia cards coming soon on the Maxwell architecture.