Both cards are in the same performance tier. Depending on the game, the differences are detectable only by a synthetic benchmark, not by actual gameplay.
Graphics card designers select the appropriate balance of specs such as shaders, clocks, vram, etc to meet a certain price/performance point.
You will get fair value at every price point. Don't stew over the decision.
Mantle allows the graphics driver to execute with less cpu overhead. It is of minor benefit when using a strong cpu like you probably have if you are considering these cards.
Vram is of value if your game needs it. Skyrim mods are notorious for consuming vram.
Past that, it is probably better to spend your vram dollars on a faster card in the first place.
Read this:
http://www.pugetsystems.com/labs/articles/Video-Card-Performance-2GB-vs-4GB-Memory-154/
As a rule, the R9 cards run hotter and take more power than their Nvidia equivalents. They get their performance by being factory overclocked. That is why they will come with fancy coolers.
Do not plan on much fro overclocking. Vendors are wise to overclocking and bin their chips. The best ones go into factory superclocked versions to be sold at a higher price. I think you gat fair value for the extra paid.
My sense is that most prefer the nvidia drivers.
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.
For the R9-280X you get 35% unfavorable.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121803
For the GTX770, you get 16% unfavorable
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121770
I might prefer this evga version:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130921