Just because something is "outdated" doesn't mean it can't perform.
Gears of War 4 (http://www.techspot.com/review/1263-gears-of-war-4-benchmarks/page4.html): Ivy Bridge i7 keeps up with Skylake i7 (despite being over4 years old), & Sandy Bridge i5 keeps up with Haswell i5 (despite being hearly 6 years old)...not to mention the 4-year-old FX-8350 keeping pace with the i5s.
Deus Ex: Mankind Divided (http://www.techspot.com/review/1235-deus-ex-mankind-divided-benchmarks/page5.html): Sandy Bridge & Ivy Bridge i5s not only keep up with their Haswell & Skylake successors, they keep up with the Haswell & Skylake i7s. And even the FX-6350 still manages to bring ~86% of a Skylake i7's performance, which is really good considering it's over 3 years old now.
Overwatch (http://www.techspot.com/review/1180-overwatch-benchmarks/page5.html): Sandy Bridge i7s easily kept up with their Skylake great-grandchildren, & Sandy Bridge i5s kept pace with their Haswell grandkids. And even though the FX chips were well below the i5s in performance, the review still pointed out that with that particular GPU you'd only see the difference with a 120/144Hz monitor.
DOOM (http://www.techspot.com/review/1173-doom-benchmarks/page5.html): Sandy Bridge/Ivy Bridge i5s again kept up not only with the Skylake i5s but with the i7s as well. Yes, the 4- and 6-core (as well as the lower-power 8-core) FX chips dropped off severely, but their performance was still more than sufficient for a 60+ FPS experience...& the FX-8370 still had ~86% of the Ivy Bridge/Haswell/Skylake i7 chips.
Dark Souls III (http://www.techspot.com/review/1162-dark-souls-3-benchmarks/page5.html): Identical performance for Sandy Bridge, Ivy Bridge, Haswell & Skylake Core i5s & i7s, with their average FPS matched by the FX-8350. The FX-6350 was right behind them (~93% of the performance), & even the FX-4320 wasn't too shabby (~85% performance).
Tom Clancy's The Division (http://www.techspot.com/review/1148-tom-clancys-the-division-benchmarks/page5.html): Across the board, pretty much every CPU they used turned in high performance, with even the lowest 2 (Haswell i3 & FX-4320) getting over 90% of the performance of the Skylake i7. Again, moving from Sandy Bridge to Haswell, or Ivy Bridge to Skylake, gave the leaders only an extra 1 or 2 FPS (or about a maximum of 3% improvement).
Rise of the Tomb Raider (http://www.techspot.com/review/1128-rise-of-the-tomb-raider-benchmarks/page5.html): Although the gap is somewhat noticeable between the Haswell & Skylake chips, the gap is still narrow enough that the Sandy Bridge & Ivy Bridge chips are still at almost 90% of that performance. And the FX chips were right there in performance with the Haswell chips for average FPS.
Those were all games released this calendar year. Yes, they generally show Intel chips having "better" performance than AMD's FX chips...but when you not only have brand-new chips that (for the most part) can only outperform your competitor's chips by a 5-10% margin, but also your own chips that are just as old generally have even less of a gap (or in many cases no gap at all), you start to wonder what the justification is for the price.
And the tier lists show that. It's why Tom's Hardware still shows Ivy Bridge & Haswell i7 chips (& some Ivy Bridge i5 chips) as being equal with the new Skylake chips, & why the Sandy Bridge i7 chips & Sandy Bridge/Ivy Bridge i5s are right behind them in performance (which also happens to be where the full-power octa-core chips are as well): not because they're concerned with how "old" a particular chip is, but because they look at the performance.
Now, if @r2j2612 (OP) was asking for suggestions on a brand-new build, then no, I wouldn't recommend an FX-based build...just like I wouldn't recommend a brand-new Haswell, Ivy Bridge or Sandy Bridge build. Although the performance is still good, there are no upgrade paths for any of those platforms: Sandy Bridge & Ivy Bridge use the discontinued LGA 1155 sockets, & their Haswell replacements' LGA 1150 sockets are also now discontinued (Skylake & Kaby Lake are using LGA 1151), just like the AM3+ socket ended with the FX chips (Zen being planned for the new AM4 socket). Nor can Sandy Bridge, Ivy Bridge, Haswell or AM3+ boards take advantage of the new DDR4 RAM. But that's the point: he isn't necessarily looking for a new build. Replacing his current CPU extends the life of his current system, for a much lower price than any conversion to Intel could possibly match (unless he's willing maybe to settle for a Skylake Pentium, or is willing to settle for one of the DDR3 Skylake boards).
Basically, it comes down to cost: he can pay up to $180 USD to improve his system with a new CPU, or pay double that to switch to Intel & only get maybe another 10% in gaming performance. Even with a new GTX 1070 & monitor, it's still $560 for a replacement CPU & the GPU vs. ~$740-750 for the GPU & the Intel switch, where he'd pay over 30% more just for maybe a 10% improvement. The question for him is whether the slight improvement is worth the cost, & whether he can even afford it.