Unfortunately that's not really true. AMD chips are cheaper, this is true, but there is a larger gap between their benchmarks and Intel benchmarks than there is between their price and Intel's price. Basically - they are less powerful than they are cheap, so they're not really good at price-per-dollar either. It's a crazy thing - all AMD did was fire their best engineers and now they're having a lot of trouble designing chips!
In general, low-end Intel chips get the nod over AMD. See:
http://arstechnica.com/gadgets/2014/12/the-ars-system-guides-gaming-boxes-december-2014/2/
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106.html
You're of course right as far as pure gaming is concerned.
Or maybe I just had bad experiences with Intel.