Performance is the difference.
Intel offers better performance, but they also cost a little more money.
AMD FX series CPUs generally cost a little less but performance is lower. The FX series CPU performance is generally equivalent to Intel's 1st generation Core i5/i7 series, perhaps a little faster. However, Intel's 2nd / 3rd / 4th generation Core i5/i7 CPU provides more performance. There are specific situations where AMD's FX CPUs can do just as well or maybe slightly better than Intel's CPUs, but that is generally limited to video encoding in certain situations.