The i7's of the same generation come stock at slightly higher clock speeds than their i5 counterparts, a difference that can be made up with a simple BIOS setting. Most benchmarks are run at stock speeds unless they specify otherwise. So no, that almost-illusory difference does not justify paying $100 more on its own.
Of course, $2000 is a very, very large budget. Its not hard to find situations where i7's really shine, they're just usually not games. It depends on what else, if anything, you want to do with this machine.
Everyone probably has their own horror stories, but AMD products are as solid and reliable as Nvidia's. Due to recent driver improvements, AMD has a card on the market now that matches every Nvidia product, and often can be found for a bit cheaper. They also tend to have extremely wide memory bandwidth compared to their Nvidia counterparts, which can be helpful in some games/monitor setups.
I don't mean to dissuade you from Nvidia necessarily, but there's no practical reason not to consider both.