r9 290 vs gtx 780

Solution
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.
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.
 
Solution
Both cards are comparable performers at a similar price.

I have a method to pick between equally performing products.
Go to newegg and find the candidates.
Filter on the most reviews by verified buyers.
Then look at what percent of the reviews have one or two eggs indicating some sort of a problem.
In particular, look at the reasons for a bad review. Some are not very valid, so exclude those.

To answer your question, this is the most popular R9-290 card:
SAPPHIRE TRI-X OC 100362-2SR Radeon R9 290 4GB 512-bit GDDR5 PCI Express 3.0 Video Card
21% of verified owners had some sort of issue.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202080
The most popular GTX780 card was the
EVGA ACX Cooler 03G-P4-2784-KR G-SYNC Support GeForce GTX 780 Superclocked 3GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130918
Only 3% of verified owners had issues.

You decide.