There's no benefit to buying it for a brand-new system.
But for those of us that are still using one, it comes down to the usual suspects: performance & money.
Money is the obvious one, in that until recently FX-based systems were much cheaper than Intel systems, & (until the 2C/4T Kaby Lake unlocked Pentiums debuted) were the cheapest way to get at least a quad-core (or at least a 2C/4T) CPU that would run games (i.e. Titanfall 2 won't run on any 2C/2T CPU, http://www.techspot.com/review/1271-titanfall-2-pc-benchmarks/page3.html), regardless of actual performance.
Performance may seem to be a strange metric. However, there is performance, as in, "This system with CPU W, RAM X, SSD Y, & GPU Z, delivers the absolute, 100% best performance that any system can currently achieve, & is the standard benchmark by which all other systems will be measured (& found wanting)"...& then there's performance as in, "My monitor can only reach X resolution with Y refresh rate, & I'm only playing group Z of older games that don't require as much horsepower, so do I really need the expensive, top-line system?" For example, my brother-in-law generally plays Rise of Nations or Earth Defense Force: Insect Armageddon (the latter being a game that my old HP laptop can play on integrated graphics); his sons also play a lot of Minecraft, & they've all rediscovered Starcraft: Brood War (now that the new patch from Blizzard makes it 100% free to play)...& that's when my nephews aren't working on their school projects. They don't even need a brand-new, Kaby Lake Pentium build, let alone a core i5/i7 or Ryzen 5/7 build, to play those games or perform their non-gaming tasks. Heck, they'd probably benefit more from installing SSDs, but my brother-in-law doesn't want to spend the time to reinstall the OS on 3 separate desktops (he's had to do that too often in the past on those systems anyway to choose to do so unnecessarily).
And that's why you will probably see FX systems hang around for a while. They were cheaper to build/buy, & they still provide "good enough" performance for a lot of people, not just non-gamers but also gamers that don't drool over having bleeding-edge technology & rebuild their systems from scratch every year.
And even in some modern games, you'd be hard-pressed to see any difference in performance between an FX chip & the newest ones. Take Dark Souls III, for example (http://www.techspot.com/review/1162-dark-souls-3-benchmarks/page5.html); because of the 60FPS cap, even an FX-8350 paired with a GTX 980Ti had no trouble maintaining an average 60FPS at 1440p resolutions. And sure, Intel performance blew the FX chips away in Overwatch (http://www.techspot.com/review/1180-overwatch-benchmarks/page5.html), but for someone like me (using a 1600x900/60Hz monitor paired with an R9 380), I wouldn't get any benefit from a "faster" Intel system. Same thing happens with DOOM (http://www.techspot.com/review/1173-doom-benchmarks/page5.html), BF1 (http://www.techspot.com/review/1267-battlefield-1-benchmarks/page2.html), For Honor (http://www.techspot.com/review/1333-for-honor-benchmarks/page3.html), & Gears of War 4(http://www.techspot.com/review/1263-gears-of-war-4-benchmarks/page4.html); my system would be held back more by the R9 380 than by the FX-8320, but the performance I would get matches up with what my monitor can provide anyway.
But....
If I had the cash & the opportunity to build a new system right now, then I wouldn't pick an FX-based system. As SR-71 pointed out, it's at End Of Life with Ryzen being released. Just like I wouldn't build a brand-new system with a Haswell chip (being also EOL).